Worded indicies problem- Find temperature of liquid

Question

When a liquid is placed into a refrigerator, its temperature T°C at a time t minutes is given by the formula

T=T*10^-kt

The temperature is initially 100°C and drops to 40°C in 5 minutes.

Find the temperature of liquid after 15 minutes.

log2x

Answer 1

I think you may have meant T = T₀*10^-kt so that you get the equation

T= 100*10^-kt so that at t=0 you get 100.

 

Now at t=5 you drop 40 to 60 so T=60. Substituting in you get

 

60 = 100*10^-5k and you can figure out k

.6 = 10^-5k

log .6 = -5k

k=log.6/(-5) = .04437

 

So your function becomes T=100*10^-.04437t

 

Now that you found that constant and have the equation, you can just substitute t=15 to get your answer.

 

T = 100 * 10^-.04437(15)

T= 21.6 degrees.

 

Hopefully I'm interpreting your problem correctly for you. Hope this helped.