Math  /  Calculus

Question9 ( 8 points). A hot cup of coffee is placed outside on a cold day. The temperature of the coffee (in degrees Fahrenheit) after tt minutes is given by the function f(t)=(36+90et.f(t)=\left(36+90 e^{-t} .\right. (a) What is limtf(t)\lim _{t \rightarrow \infty} f(t) ?

Studdy Solution
Determine the limit of the entire function f(t)=36+90et f(t) = 36 + 90 e^{-t} as t t \rightarrow \infty .
Since et0 e^{-t} \rightarrow 0 as t t \rightarrow \infty , the term 90et 90 e^{-t} also approaches zero. Therefore, the function simplifies to:
limtf(t)=36+900=36 \lim_{t \rightarrow \infty} f(t) = 36 + 90 \cdot 0 = 36
The limit of f(t) f(t) as t t \rightarrow \infty is 36 \boxed{36} .

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