Question

A solid object is dropped into a pond with a temperature of 20 degrees Celsius. The function f(t)=Ce(−kt)+20 represents the situation, where t is time in minutes, C is a constant, and k=0.0399. After 4 minutes the object has a temperature of 35 degrees Celsius. What was the initial temperature of the object? Round your answer to the nearest tenth, and do not include units.

Answer 1

Answer:

The initial temperature of the object was 37.6 degrees Celsius

The initial temperature of the object was 37.6 (without units)

Step-by-step explanation:

we have

$f(t)=Ce^{(-kt)} +20$

where

f(t) represent the temperature of the object in degree Celsius

t is the time in minutes

Find the value of the constant C

we have the ordered pair (4,35)

substitute in the equation and solve for C

$35=Ce^{(-0.0399*4)} +20$

$Ce^{(-0.0399*4)}=15$

$C=15/e^{(-0.0399*4)}$

$C=17.6$

Find the initial value of the object

we know that

The initial temperature is the value of f(t) when the value of t is equal to zero

so

For t=0

$f(0)=(17.6)e^{(-k*0)} +20$

$f(0)=17.6 +20$

$f(0)=37.6\ degrees\ Celsius$

therefore

The initial temperature of the object was 37.6 degrees Celsius

The initial temperature of the object was 37.6 (without units)