Question

there are currently 260 people in archery clubs across the city, and this number is increasing by 11% per year. Enter an equation that can be used to find the number of people, y, in archery clubs across the city after 8 years.

Answer 1

The equation to find the number of people in archery clubs after 8 years with an 11% annual increase is y = 260(1 + 0.11)^8.

Step-by-step explanation:

To find the number of people, y, in archery clubs across the city after 8 years given an initial population of 260 people and an annual increase of 11%, we can use the formula for exponential growth, which is y = P(1 + r)^t. In this formula, P represents the initial number of people, r represents the growth rate as a decimal, and t represents the time in years.

The equation that can be used in this scenario would be y = 260(1 + 0.11)^8.

Answer 2

Given :

There are currently 260 people in archery clubs across the city, and this number is increasing by 11% per year.

To Find :

An equation that can be used to find the number of people, y, in archery clubs across the city after 8 years.

Solution :

Increase in people after 1 years :

`P = 260 + 260* 0.11\\\\P = 260( 1 + 0.11)\\\\P = 260* 1.11`

After 2 years :

`P = 260* 1.11 + 260* 1.11* 0.11\\\\P = 260* 1.11 ( 1 + 0.11)\\\\P = 260* 1.11^2`

Therefore, after 8 years the expression of population is :

`P = 260* 1.11^8`

Hence, this is the required solution.