Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The expression
11(1.022)^(t) models the per capita gross domestic product (GDP) of the US, in thousands of dollars, as a function of the number of years since 1950 .
What does 1.022 represent in this expression?
Choose 1 answer:
(A) The per capita GDP in the US was
$1022 in 1950.
(B) The maximum per capita GDP occurred 1.022 years after 1950 .
(C) The per capita GDP in the US is multiplied by approximately 1.022 each year.

The expression $11(1.022)^{t}$ models the per capita gross domestic product (GDP) of the US, in thousands of dollars, as a function of the number of years since $1950$ . $\newline$ What does $1$ . $022$ represent in this expression? $\newline$ Choose $1$ answer: $\newline$ (A) The per capita GDP in the US was $\$ 1022$ in $1950$ . $\newline$ (B) The maximum per capita GDP occurred $1$ . $022$ years after $1950$ . $\newline$ (C) The per capita GDP in the US is multiplied by approximately $1$ . $022$ each year.

View step-by-step help

View step-by-step help

Evaluate two-variable equations: word problems

Full solution

Q. The expression

11(1.022)^{t}

models the per capita gross domestic product (GDP) of the US, in thousands of dollars, as a function of the number of years since

1950

.

\newline

What does

1

.

022

represent in this expression?

\newline

Choose

1

answer:

\newline

(A) The per capita GDP in the US was

\$ 1022

in

1950

.

\newline

(B) The maximum per capita GDP occurred

1

.

022

years after

1950

.

\newline

(C) The per capita GDP in the US is multiplied by approximately

1

.

022

each year.

Nature of Expression: The expression given is $11(1.022)^{t}$ , where $t$ represents the number of years since $1950$ . To understand what $1.022$ represents, we need to consider the nature of the expression. This is an exponential function, where the base of the exponent $(1.022)$ indicates the rate of change per year.
Analysis of Options: If we look at the options provided, we can analyze each one: $\newline$ (A) Suggests that the per capita GDP was $\$1022$ in $1950$ . However, the number $11$ in the expression is the coefficient that would represent the initial value in $1950$ , not $1.022$ . $\newline$ (B) Suggests that the maximum per capita GDP occurred $1.022$ years after $1950$ . This does not make sense in the context of the expression, as $1.022$ is not a measure of time but a growth factor. $\newline$ (C) Suggests that the per capita GDP in the US is multiplied by approximately $1.022$ each year. This aligns with the nature of an exponential growth model, where the base of the exponent represents the growth rate.
Conclusion: Based on the analysis, we can conclude that $1.022$ represents the annual growth factor of the per capita GDP. This means that each year, the per capita GDP is multiplied by $1.022$ , indicating an approximate $2.2\%$ increase per year (since $1.022$ is approximately $1 + 0.022$ , and $0.022$ is $2.2\%$ ).

More problems from Evaluate two-variable equations: word problems

Question

b(t)

gives the temperature (in degrees Celsius) of a pan of brownies by time

t

\newline

\int_{0}^{6} b^{\prime}(t) d t=93

\newline

1

\newline

t=6

minutes, the temperature of the brownies is

93

degrees Celsius.

\newline

t=6

minutes, the brownies have an instantaneous rate of temperature change of

93

degrees Celsius per minute.

\newline

(C) During the first six minutes, the temperature of the brownies increases an average of

93

degrees Celsius per minute.

\newline

(D) The temperature of the brownies increased by

93

degrees Celsius in the first six minutes.

Posted 7 months ago

Question

The number of subscribers to a magazine is changing at a rate of

r(t)

subscribers per month (where

t

is time in months).

\newline

\int_{8}^{10} r^{\prime}(t) d t=7

\newline

1

\newline

(A) As of month

10

, the magazine had

7

\newline

(B) The average rate of change in subscribers between month

8

10

7

subscribers per month.

\newline

(C) The number of subscribers increased by

7

t=8

t=10

\newline

(D) The rate of change of number of subscribers increased by

7

subscribers per month between

t=8

t=10

Posted 7 months ago

Question

A grocery store receives a shipment of bananas. The percent of the shipment that is still suitable for sale is decreasing at a rate of

r(t)

percent of the original shipment per day (where

t

is the time in days). At

t=2

, the grocery store found

85 \%

of the shipment to be suitable for sale.

\newline

0.85+\int_{2}^{4} r(t) d t=0.6 \text { mean? }

\newline

1

\newline

(A) As of the fourth day,

60 \%

of the bananas suitable on the second day are still suitable.

\newline

(B) Between the second and fourth days,

60 \%

of the remaining bananas became unsuitable for sale per day.

\newline

(C) Between the second and fourth day, another

60 \%

of the bananas became unsuitable for sale.

\newline

(D) As of the fourth day,

60 \%

of the shipment was still suitable for sale.

Posted 7 months ago

Question

The number of people exposed to a certain illness is increasing at a rate of

r(t)

people per day (where

t

is the time in days). At

t=12

115

people exposed to the illness.

\newline

115+\int_{12}^{20} r(t) d t

\newline

1

\newline

(A) The change in the number of people exposed to the illness between days

12

20

\newline

(B) The change in the rate at which people are exposed to the illness between days

12

20

\newline

(C) The time it takes for

20

more people to be exposed to the illness

\newline

(D) The number of people exposed to the illness at

t=20

Posted 7 months ago

Question

The population of a town grows at a rate of

r(t)

people per year (where

t

is time in years). At

t=3

, the town's population was

1000

\newline

1000+\int_{3}^{8} r(t) d t=1500

\newline

1

\newline

(A) The town's population grew by

1500

t=3

t=8

\newline

(B) The town's population grew at a rate of

1500

people per year at

t=8

\newline

(C) The average rate at which the population grew between

t=3

t=8

1500

people per year.

\newline

t=8

, the town's population was

1500

Posted 7 months ago

Question

The value of a computer is decreasing at a rate that is proportional at any time to the value of the computer at that time.

\newline

The computer is worth

\$ 850

initially, and it is worth

\$ 306

2

\newline

How much will the computer be worth after

5

\newline

1

\newline

\$ 0

\newline

\$ 66

\newline

\$ 79

Posted 7 months ago

Question

Carbon dating involves the measurement of the amount of carbon

-14

in a sample. Archaeologists sometimes use carbon dating to estimate the number of years since an organism died. The function shows the ratio,

R(t)

-14

remaining in a sample to the original amount of carbon

-14

t

\newline

R(t)=2^{-0.00175 t}

\newline

If one sample was

3

times as old as another sample of the same material, how would the carbon

-14

ratios of the samples relate?

\newline

1

\newline

(A) The ratio of the older sample would be

3

times the ratio of the newer sample.

\newline

(B) The ratio of the newer sample would be

3

times the ratio of the older sample.

\newline

(C) The ratio of the older sample would be the cube of the ratio of the newer sample.

\newline

(D) The ratio of the newer sample would be the cube of the ratio of the older sample.

Posted 7 months ago

Question

The average production cost for major movies is

67

million dollars and the standard deviation is

23

million dollars. Assume the production cost distribution is normal. Suppose that

46

randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to

4

decimal places where possible.

\newline

a. What is the distribution of

X

\newline

X \sim N(67, 23^2)

\newline

b. What is the distribution of

\bar{x}

\newline

\bar{x} \sim N\left(67, \left(\frac{23}{\sqrt{46}}\right)^2\right)

\newline

c. For a single randomly selected movie, find the probability that this movie's production cost is between

69

73

million dollars.

\newline

23

0

\newline

d. For the group of

46

movies, find the probability that the average production cost is between

69

73

million dollars.

23

4

\newline

e. For part d), is the assumption of normal necessary?

\newline

\newline

\newline

23

5

Posted 7 months ago

Question

3

\newline

\newline

\newline

3

-51

(Algo) Multiproduct CVP Analysis (LO

3

-4

\newline

1

11

\newline

\newline

\newline

\newline

\newline

\newline

\newline

Georgeland Cycles makes and sells two models of electric bicycles. The Commuter (a folding model) sells for

\$2,503.00

\newline

X (a fat-tire trail model) sells for

\$4,503.00

. Unit variable costs for the Commuter are

\$1,753.00

and for the Tour

\newline

\$3,203.00

. Annual fixed costs at Georgeland are

\$488,050

. The marketing manager estimates that the annual mix of sales is

30

percent Commuter model and

70

percent Touring model.

\newline

\newline

a. How many of each model ebike must Georgeland Cycles sell every year to break even?

\newline

b. How many of each model ebike must Georgeland Cycles sell every year to earn operating profits of

\$102,150

\newline

Complete this question by entering your answers in the tabs below.

\newline

\newline

\newline

\newline

How many of each model ebike must Georgeland Cycles sell every year to break even?

\newline

\newline

\newline

\newline

\newline

\newline

Break-even ebikes

\newline

\newline

\newline

Posted 7 months ago

Question

Apply the distributive property to factor out the greatest common factor.

\newline

25 p+50 q=

\newline

\square

Posted 17 hours ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant