Chapter 4.3, Problem 7E

Reminder Round all answers to two decimal places unless otherwise indicated.

A Coin Collection The value of a coin collection increases as new coins are added and the value of some rare coins in the collection increases. The value V, in dollars, of the collection t years after the collection was started is given by the following table.

$t=\text{time,}\text{in}\text{years}$	$V=\text{value,}\text{in}\text{dollars}$
$0$	$130.00$
$1$	$156.00$
$2$	$187.20$
$3$	$224.64$
$4$	$269.57$

a. Show that these data are exponential.

b. Find an exponential model for the data.

c. According to the model, when will the collection have a value of $\$500$?