Question

Please assist me in knowing how to figure these out.

Answer 1

we have the equation

`H(t)=180-a(108)^(-t)`

A) since H is an exponential function 180 represents the maximum posible value of H or the maximum temperature that the center of the cake can reach

b)

we have

H(t)= 22° C

when placed in the oven or t=0

`22=180-a(108)^0`
`22=180-a(1)`
`a=180-22=158`

the value of a is 158

C)

H(t)=150°C

we already know a=158

let's solve for t

`150=180-(158)(1.08)^(-t)`
`-30=-(158)(1.08)^(-t)`
`(30)/(158)=1.08^(-t)`
`ln((30)/(158))=ln(1.08^(-t))`
`ln((30)/(158))=-t*ln(1.08)`
`-t=(ln((30)/(158)))/(ln(1.08))`
`t=-(ln((30)/(158)))/(ln(1.08))=21.587`

now this is the time 29 minutes before taking the cake out of the oven

so the total time is 29+21.587

then the total time the baking thin was in the oven

is 50.587 minutes