Question

Kwame bought a car for $25,000. The value of the car is decreasing at a rate of 6.5% each year. Write a function that represents the price P of the car after x years. Note: use parentheses around the rate

Answer 1

The function that represents the price P of the car after x years is:

$P = 25000(0.935)^x$

Solution:

The decreasing function is given as:

$y = a(1 - r)^t$

Where,

y is future value

a is initial value

r is decreasing rate in decimal

t is time period

From given,

a = 25000

$r = 6.5 \% = \frac{6.5}{100} = 0.065$

number of years = x

future value = P

Therefore,

$P = 25000(1 - 0.065)^x\\\\P = 25000(0.935)^x$

Thus the function is found