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}$$-30=-(158)(1.08)^{-t}$$\frac{30}{158}=1.08^{-t}$$ln(\frac{30}{158})=ln(1.08^{-t)}$$ln(\frac{30}{158})=-t*ln(1.08)$$-t=\frac{ln(\frac{30}{158})}{ln(1.08)}$$t=-\frac{ln(\frac{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