Question

The number of subscribers y to a newspaper after t years is shown by the equation below.

y = 75(0.95)^t

Which conclusion is correct about the number of subscribers to the newspaper?

It increased by 75% every year.

It decreased by 75% every year.

It increased by 5% every year.

It decreased by 5% every year.

Answer 1

Option 4 - It decreased by 5% every year.

Explanation:

Given : The number of subscribers y to a newspaper after t years is shown by the equation
`y = 75(0.95)^t`

To find : Which conclusion is correct about the number of subscribers to the newspaper?

Solution :

Equation -
`y = 75(0.95)^t`

where y is the subscribers to a newspaper and t is the time in years.

Comparing the given equation with the exponential equation

75 is the initial number of subscribers to a newspaper and t is the time period is years.

And their is an exponential decay function with rate r=0.05=5% (1-0.95=0.05)

This all imply that :

The number of subscribers to a newspaper decreased by 5% every year.

Therefore, Option 4 is correct.

Answer 2

Answer: It decreased by 5% every year.

Explanation:-

The number of subscribers y to a newspaper after t years is shown by the equation
`y=75(0.95)^t`, where 75 is the initial number of subscribers to a newspaper and t is the time period is years.

The above equation can be rewrite as

`75(1-0.05)^t` which is equivalent to the exponential decay function with rate r=0.05=5%

⇒ The number of subscribers to a newspaper decreased by 5% every year.

⇒ Fourth option is correct.