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The number of subscribers to a magazine is changing at a rate of
r(t) subscribers per month (where
t is time in months).
What does
int_(8)^(10)r^(')(t)dt=7 mean?
Choose 1 answer:
(A) As of month 10 , the magazine had 7 subscribers.
(B) The average rate of change in subscribers between month 8 and month 10 was 7 subscribers per month.
(C) The number of subscribers increased by 7 between
t=8 and
t=10 months.
(D) The rate of change of number of subscribers increased by 7 subscribers per month between
t=8 and
t=10 months.

The number of subscribers to a magazine is changing at a rate of $r(t)$ subscribers per month (where $t$ is time in months). $\newline$ What does $\int_{8}^{10} r^{\prime}(t) d t=7$ mean? $\newline$ Choose $1$ answer: $\newline$ (A) As of month $10$ , the magazine had $7$ subscribers. $\newline$ (B) The average rate of change in subscribers between month $8$ and month $10$ was $7$ subscribers per month. $\newline$ (C) The number of subscribers increased by $7$ between $t=8$ and $t=10$ months. $\newline$ (D) The rate of change of number of subscribers increased by $7$ subscribers per month between $t=8$ and $t=10$ months.

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Evaluate two-variable equations: word problems

Full solution

Q. 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

What does

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

mean?

\newline

Choose

1

answer:

\newline

(A) As of month

10

, the magazine had

7

subscribers.

\newline

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

8

and month

10

was

7

subscribers per month.

\newline

(C) The number of subscribers increased by

7

between

t=8

and

t=10

months.

\newline

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

7

subscribers per month between

t=8

and

t=10

months.

Understand the expression: Understand the integral expression. $\newline$ The integral of $r'(t)$ from $8$ to $10$ represents the total change in the number of subscribers from month $8$ to month $10$ .
Interpret the result: Interpret the result of the integral. $\newline$ Since the integral of the rate of change of subscribers, $r'(t)$ , over the interval from $t=8$ to $t=10$ is equal to $7$ , this means that the total change in the number of subscribers over these two months is $7$ subscribers.
Match interpretation to options: Match the interpretation to the given options. $\newline$ The correct interpretation of the integral result is that the number of subscribers increased by $7$ between $t=8$ and $t=10$ months. This matches option (C).
Eliminate incorrect options: Eliminate other options based on the interpretation. $\newline$ Option (A) is incorrect because the integral does not provide information about the total number of subscribers at any point in time. $\newline$ Option (B) is incorrect because the integral gives the total change, not the average rate of change. $\newline$ Option (D) is incorrect because the integral gives the total change in subscribers, not the change in the rate of change.

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Question

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

\newline

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

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