find initial tempeture

Question

A deli sandwich is placed inside a cooler. As the sandwich cools, its temperature C(t)

 in degrees Celsius after t

 minutes is given by the following exponential function.

C(t)=25(0.89)^t

Find the initial temperature.

Does the function represent growth or decay?

By what percent does the temperature change each minute?

Answer 1

C(t)=25(0.89)^t

Exponential equation:

C(t) = C₀ (1- r)^t

C(t): temperature in degrees Celsius after t minutes

C₀: initial temperature

r: rate

1 - r: factor. If factor < 1, then is a decay. If factor > 1, then is growth

t: number of minutes

In this case:

Initial temperature: C₀ = 25 C

Factor: 0.89 < 1 the function represents a Decay

Rate:

1 - r = 0.89

-r = 0.89 - 1

-r = -0.11

r = 0.11

rate = 11% each minute

Answer 2

Hello, Carolina,

Given the temperature as a function of time is:

C(t)=25(0.89)^t

when t = 0, C(0) = 25(0.89)⁰, or -25(1) = 25C

The function shows a decay, since (0.89)^t becomes increasingly small as t gets larger. For t = 10 minutes, (0.89)¹⁰ equates to 0.312, for example.

The temperature changes by 0.89, or 89%, every minute.

Bob