Question

The price of a gallon of milk at a particular convenience store has been recorded over the course of 10 weeks. At the end of the third week, the price $3.38 and at the end of the eighth week the price is $3.55. The price has been observed to increase exponentially.

Answer 1

Given:

The price of milk at the end of the third week = $3.38.

The price of milk at the end of the eighth week = $3.55.

To find:

The approximate increase in price of milk per week and the cost of milk at the end of the tenth week.

Solution:

To determine the increase in the price per week, we divide the difference in price over n number of weeks by n.

Here we know the prices of milk at the end of the third and the eighth week. There are 5 weeks between these two.

The approximate increase in the price of milk
`= (3.55-3.38)/(5) = (0.17)/(5) = 0.034.`

So there is an increase of $0.034 per week.

To determine the price at the end of the tenth week, we add the increase in price over two weeks to the price at the end of the eighth week.

The price of milk at the end of the eighth week = $3.55.

The increase in price over two weeks
`=2(0.034) = 0.068.`

The price of the milk at the end of the tenth week
`= 3.55+0.068=3.618.`

Rounding this off to the nearest cent, we get the price of milk at the end of the tenth week is $3.62.