Question

question 7 of 7
a can of soda is placed inside a cooler. as the soda cools, its temperature c(t) in degrees celsius after t minutes is given by the following exponential function.
c(t) = 26(0.94)^t
find the initial temperature.
______ °c
does the function represent growth or decay?
○ growth ○ decay
by what percent does the temperature change each minute?
______ %

Explanation:

Step1: Find initial temperature (t=0)

Substitute $t=0$ into $C(t)=26(0.94)^t$. Any number to the power of 0 is 1, so:
$C(0)=26(0.94)^0=26\times1=26$

Step2: Identify growth/decay

Check the base of the exponent: $0.94<1$, so this is decay.

Step3: Calculate percent change

The decay factor is $0.94$, so the percent change is $1 - 0.94 = 0.06$, which is $6\%$ (a decrease, so a 6% change each minute).

Answer:

Initial temperature: $26$ °C
Function represents: decay
Percent change each minute: $6$ %