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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?

The price of 9-volt batteries is increasing according to the function below,where-example-1
User Doovers
by
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1 Answer

21 votes
21 votes

Step-by-step 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} \\ (5)/(1.1)=e^(0.047t) \\ take\text{ the natuaral logarithm of both sides} \\ ln((5)/(1.1))=ln(e^(0.047t)) \\ ln((5)/(1.1))=0.047t \\ t=ln((5)/(1.1))/0.047 \\ 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.

User Terrick
by
2.7k points
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