Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Poultry should be cooked to a temperature of
75^(@)C. A chicken is removed from the oven and left to rest in a room that is at a constant temperature of
22^(@)C. The temperature of the chicken
t hours after it is removed from the oven is given by the exponential function:

T(t)=22+53(0.74)^(t)
What is the approximate temperature of the chicken after 2 hours?
Choose 1 answer:
(A)
22^(@)C
(B)
51^(@)C
(c)
74^(@)C
(D)
75^(@)C

Poultry should be cooked to a temperature of $75^{\circ} \mathrm{C}$ . A chicken is removed from the oven and left to rest in a room that is at a constant temperature of $22^{\circ} \mathrm{C}$ . The temperature of the chicken $t$ hours after it is removed from the oven is given by the exponential function: $\newline$ $T(t)=22+53(0.74)^{t}$ $\newline$ What is the approximate temperature of the chicken after $2$ hours? $\newline$ Choose $1$ answer: $\newline$ (A) $22^{\circ} \mathrm{C}$ $\newline$ (B) $51^{\circ} \mathrm{C}$ $\newline$ (C) $74^{\circ} \mathrm{C}$ $\newline$ (D) $75^{\circ} \mathrm{C}$

View step-by-step help

View step-by-step help

Compare linear and exponential growth

Full solution

Q. Poultry should be cooked to a temperature of

75^{\circ} \mathrm{C}

. A chicken is removed from the oven and left to rest in a room that is at a constant temperature of

22^{\circ} \mathrm{C}

. The temperature of the chicken

t

hours after it is removed from the oven is given by the exponential function:

\newline

T(t)=22+53(0.74)^{t}

\newline

What is the approximate temperature of the chicken after

2

hours?

\newline

Choose

1

answer:

\newline

(A)

22^{\circ} \mathrm{C}

\newline

(B)

51^{\circ} \mathrm{C}

\newline

(C)

74^{\circ} \mathrm{C}

\newline

(D)

75^{\circ} \mathrm{C}

Identify function and value: Identify the given function and the value to be substituted. $\newline$ The temperature function is given by $T(t) = 22 + 53(0.74)^t$ . We need to find the temperature after $2$ hours, so we will substitute $t = 2$ into the function.
Substitute value into function: Substitute $t = 2$ into the function to find $T(2)$ . $\newline$ $T(2) = 2^2 + 53(0.74)^2$
Calculate exponent: Calculate the value of $(0.74)^2$ . $\newline$ $(0.74)^2 = 0.5476$ (rounded to four decimal places for precision)
Multiply by constant: Multiply $53$ by $0.5476$ . $\newline$ $53 \times 0.5476 = 29.0228$
Add to initial value: Add $22$ to the result from Step $4$ to find $T(2)$ . $\newline$ $T(2) = 22 + 29.0228$ $\newline$ $T(2) = 51.0228$
Round to nearest whole number: Round the result to the nearest whole number to match the answer choices. $\newline$ $T(2) \approx 51^{\circ}C$

More problems from Compare linear and exponential growth

Question

Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits

x

days to pick up the motorcycle.

\newline

Write an equation for the function. If it is linear, write it in the form

g(x) = mx + b

. If it is exponential, write it in the form

g(x) = a(b)^x

\newline

g(x) = \underline{\hspace{3em}}

Posted 10 months ago

Question

f(t)=-2t-7

change over the interval from

t=-7

t=-6

\newline

\newline

\left[\text{f(t) decreases by } 2\right]

\newline

\left[\text{f(t) increases by } 2\right]

\newline

\left[\text{f(t) increases by } 200\%\right]

\newline

\left[\text{f(t) decreases by a factor of } 2\right]

Posted 11 months ago

Question

g(t)=9^t

change over the interval from

t=1

t=3

\newline

\newline

\left[\text{g(t) decreases by a factor of } 81\right]

\newline

\left[\text{g(t) increases by a factor of } 81\right]

\newline

\left[\text{g(t) increases by } 18\%\right]

\newline

\left[\text{g(t) decreases by } 9\%\right]

Posted 10 months ago

Question

Both of these functions grow as

x

gets larger and larger. Which function eventually exceeds the other?

\newline

\newline

(A)f(x) = 8x + 3.3

\newline

(B)g(x) = 3.3^x - 5

Posted 11 months ago

Question

Both of these functions grow as

x

gets larger and larger. Which function eventually exceeds the other?

\newline

\newline

(A) \ f(x) = 2x + 9

\newline

(B)\ g(x) = 2^x

Posted 11 months ago

Question

f(x)

g(x)

are differentiable.

\newline

h(x)

h(x)=\frac{g(x)}{f(x)}

\newline

f(8)=1

f'(8)=-6

g(8)=8

g'(8)=-10

h'(8)

\newline

Simplify any fractions.

\newline

h'(8)=

Posted 11 months ago

Question

p(x)

q(x)

are differentiable.

\newline

r(x)

r(x)= \frac{p(x)}{q(x)}

\newline

p(3)= 2

p'(3)= 4

q(3)= 6

q'(3)= 9

r'(3)

\newline

Simplify any fractions.

\newline

r'(3)=

Posted 1 year ago

Question

u(x)

v(x)

are differentiable.

\newline

w(x)

w(x)= \frac{u(x)}{v(x)}

\newline

u(5)= 3

u'(5)= -2

v(5)= 7

v'(5)= 1

w'(5)

\newline

Simplify any fractions.

\newline

w'(5)=

Posted 1 year ago

Question

a(x)

b(x)

are differentiable.

\newline

c(x)

c(x)= \frac{a(x)}{b(x)}

\newline

a(2)= 4

a'(2)= 5

b(2)= 1

b'(2)= -3

c'(2)

\newline

Simplify any fractions.

\newline

c'(2)=

Posted 1 year ago

Question

m(x)

n(x)

are differentiable.

\newline

o(x)

o(x)= \frac{m(x)}{n(x)}

\newline

m(7)= 2

m'(7)= -1

n(7)= 4

n'(7)= 8

o'(7)

\newline

Simplify any fractions.

\newline

o'(7)=

Posted 1 year ago

Related topics

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