Question

In 2005, the Summerville Journal had 110,000 subscriptions. The number of subscriptions subsequently decreased by 8% each year. Write and use an exponential decay function to find the number of subscriptions in 2022

Answer 1

Answer:

The number of subscription will be 26,655 in 2022.

Step-by-step explanation:

In 2005, the number subscription is 110,000 and it is decreased at a rate 8% per year.

After 1 year number of subscription is 110,000- 8% of 110,00

                                                              =110,000(1-8%)

After 2 years  number of subscription is 110,000(1-8%) -8% of 110,000(1-8%)

                                                               =110,000(1-8%)(1-8%)

                                                               =110,000(1-8%)²

After 2 years  number of subscription is 110,000(1-8%)² -8% of 110,000(1-8%)²

                                                               =110,000(1-8%)²(1-8%)

                                                               =110,000(1-8%)³

....

and so on.

After t year the number of subscription is

$S(t)=110,000(1-8\%)^t$

t= 2022-2005=17 years

$\therefore S(t)=110,000(1+0.08)^{17}$

          ≈26,655

The number of subscription will be 26,655 in 2022.