Question

The price of 9-volt batteries is increasing according to the function `P(t) = 1.1e^(0.047t)` , where `t` is years after January 1, 1980. During what year will the price reach $5?

Answer 1

The price of 9-volt batteries reach `$5` in the year `2012`.

Explanation:

Let the price of 9-volt batteries reach `$5` aafter `t` tears,

Then `P(t)=1.1xxe^(0.047t)=5`

and hence `e^(0.047t)=5/1.1`

and `0.047t=ln(5/1.1)=ln5-ln1.1=1.609438-0.095310=1.514128`

and `t=31.215`

Hence the price of 9-volt batteries will reach `$5` in the year `1980+32=2012`