Question

The cost to rent a dvd has decreased 25% per year over the past several years if the current cost is $2 write an exponential equation describing this situation, what did it cost to rent a DVD 5 years ago

Answer 1

y = x(0.75)^t

the cost to rent a dvd 5 years ago is $8.43

Explanation:

Let x represent the cost to rent a dvd 5 years ago;

And y the cost to rent a dvd t years after.

The cost to rent a dvd has decreased 25% per year, this can be written as an exponential function;

y = x(100% -25%)^t

y = x(1-0.25)^t

y = x(0.75)^t .....1

if the current cost is $2;

t = 5 years

y = $2

Substituting the values into equation 1;

2 = x(0.75)^5

2 = x(0.2373046875)

x = 2/(0.2373046875)

x = 8.427983539094

x = $8.43