Expert: Richard J. Raridon - 4/4/2007

Question
Hi Richard I have a couple more problems I am stuck on. We have just started doing logarithms. Here is the first problem I can't figure out.

Vehicle theft in the United States has been growing exponentially since 1972. The number of stolen vehicles, in millions is given by f(x)=.88(1.03)^x, where x=0 represents the year 1972. Find the number of vehicles stolen in 1980. Note: We will use the notation log_a for thr logarithm, base a.
I got an answer of 1.1 million by plugging the number 8 into the equation for x, but I am not sure what the NOTE: part of the problem means.

The second question is, Suppopse $8,000 is available today and $10,000 is needed 10 years from now. What interest rate, compounded continuously, is needed to achieve this result? The formula for continuous compounding interest is A=P(e)^rt, P=principal, r=decimal form of annual rate, t=# of years. I thought the formula 10,000=8,000(e)^r(10) would work but I am not sure and I can't figure out how to solve this with my graphing calculator.

Please help!!!!

Answer
You don't have to use logs if your calculator will do exponentials.  1.1 million is correct
You don't need a graphing calculator to calculate one point.
By the way, don't put commas in your equations
10000 = 8000e^10r
1.25 = e^10r
ln(1.25) = 10r, r = 0.0223 or 2.23% interest