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 Question from Paul, a parent: The value of a stamp was 0.03 in 1851. The value in 2011 is $\$50,000.$If the value increased exponentially, what is the annual growth rate? Hi Paul, I am going to let$t$be the time in years where$t = 0$in 1851. Since the value$V$in dollars increases exponentially the value is $V = A e^{r \; t}$ where$A$and$r$are constants.$r$is called the exponential growth rate. Since$e^0 = 1$at time$t = 0, V = A e^0 = A$and hence$A$is the value of the stamp at time$t = 0,$that is in 1851. Hence $V = 0.03 e^{r \; t}.$ What is$t$in the year 2011? The value then is$\$50,000.$ Solve for $r.$

I hope this helps,
Penny

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