Question

Between 2005 and 2010 the average rate of inflation was about 3.3 percent per year if a cart of groceries cost 150 dollars in 2005 what did it cost in 2010

Answer 1

The products did cost $173.9 in 2010

Explanation:

Exponential function

Two variables y and x are related as an exponential function if they comply:

`F=Cr^(kx)`

where C is the initial value of F, r is the ratio, and k is a proportional constant.

The situation described in the question is modeled as

`F=Cr^(n)`

Where F is the final value of the cart of groceries in 2010, C = $150 is its value in 2005, r is the yearly rate of increase. n is the number of years

`\displaystyle r=1+(3\%)/(100\%)= 1.03`. So

`F=150\ 1.03^(n)`

If we set n=5 (from 2005 to 2010):

`F=150\ 1.03^(5)`

`F=\$173.9`

The products did cost $173.9 in 2010