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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) $75^{\circ} \mathrm{C}$

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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. $\newline$ $T(2) \approx 51^{\circ}C$

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