An item costs $4.50, and its price increases by 3.5% each year.

Question

Write a function in terms of  that represents the situation.

Answer 1

An inrease of 3.5% means that each year's total is 103.5% of the year before, right?

Year 1 = 4.5(1.035) = 4.66

Year 2 = 4.66(1.035) = 4.82

etc.

So, year 2 is 4.5(1.035)(1.035) = 4.82

Multiplying something by itself can be written with an exponent instead, so 2 years is...

4.5(1.035)²

Since the number of years is the variable (let's call it t)...

4.5(1.035)^t