Question

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

Answer 1

Explanation

The price model is given by the exponential equation below.

$P(t)=1.1e^^{0.047t}$

When the price becomes $, we will have;

$\begin{gathered} 5=1.1e^{0.047t} \\ Divide\text{ both sides by 1.1} \\ \frac{5}{1.1}=e^{0.047t} \\ take\text{ the natuaral logarithm of both sides} \\ ln(\frac{5}{1.1})=ln(e^{0.047t}) \\ ln(\frac{5}{1.1})=0.047t \\ t=ln(\frac{5}{1.1})\div0.047 \\ t=32.22\text{ years} \end{gathered}$

Therefore, by adding 32 to the years 1980. The batteries will cost 5$ in the year

Answer: 2012.