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

A. 2016
B. 2008
C. 2004
D. 2012

Answer 1

\[\large P(t)=5=1.1e^{0.047t}\]
\[\large e^{0.047t}=\frac{5}{1.1}\]
Taking natural logs of both sides, we get:
\[\large 0.047t=\ln \frac{5}{1.1}=\ln 4.54545\]
Therefore the required value of t is given by:
\[\large t=\frac{\ln 4.54545}{0.047}=you\ can\ calculate\]

Answer 2

Don't forget to add the value of t to 1980 to find the year.