Problem Solving

Question

Xavier purchases a new computer. Each year the value of the computer will be 0.7 times the previous year's value. Write and simplify an expression that shows what value to multiply the original price by after four years. Explain.

Answer 1

This is a depreciation problem where the value decreases by 30% each year exponentially. So the factor to multiply the original value by is 0.7ⁿ, where n is the number of years after purchase.

Answer 2

Answer 3

Formula for Exponential Functions

y=ab^x

Formula for an Exponential Decay Problem

y = a(1 – r)^t

y = amount after a period of time

a = initial amount

b = (1 – r)

r = decay/depreciation rate

t = time (the variable t is used for time rather than x)

Therefore,

y = a(1 - .3)^4

Write and simplify an expression that shows what value to multiply the original price by after four years. Explain

a(1 - 0.3)^4

a * 0.7^4

0.2401a

Because “each year the value of the computer will be 0.7 times the previous year's value”, we know the depreciate rate is 0.3 or 30%. The original price will be multiplied by the quantity of one minus the depreciation rate raised to the 4^th power. The value to multiply the original price by after 4 years is 0.2401