The price of 9-volt batteries is increasing according to the function below, where t is years after January 1, 1980. During what year will the price reach $5?

P(t) = 1.1 e0.047t

Question

The price of 9-volt batteries is increasing according to the function below, where t is years after January 1, 1980. During what year will the price reach $5?

P(t) = 1.1  e0.047t

anonymous · Answer

P(t) = 1.1  e^0.047t

anonymous · Answer

Substitute P(t)=5 and solve for t

anonymous · Answer

so the setup of it would be 5=1.1*e^o.o47t? but im not good at exponents and have no idea how to figure this out

anonymous · Answer

Yeah. So first u bring the 1.1 over to the left hand side .
5/1.1= e^0.047t
Apply natural logarithm to both side you get
ln (5/1.1) = ln e^0.047t
Bring the power of ln e^0.047t to the front
ln (5/1.1)= 0.047t ln e
Ln e = 1
ln (5/1.1)=0.047t
t= (ln(5/1.1))/0.047
=32.2

anonymous · Answer

oh i see now.. thanks. imma write this down on some paper so i have some reference in case i come to another problem like this. thanks again

anonymous · Answer

no problem :D