Question

Your friend asks you to help him with his dog grooming business and will pay you 4 pennies for the first job. You agree to help if he quadruples your payment for each job completed. After 2 grooming jobs, you will receive 16 pennies, and after 3 grooming jobs, you will receive 64 pennies. Complete and solve the equation that finds the number of pennies he will pay you after the 9th dog grooming job.

Answer 1

You will receive 262,144 pennies after completing the 9th job.

Explanation:

Given:

Payment for 1st job = 4 pennies

The payment is quadrupled after this for each job completed.

Payment after 2 jobs = 16 pennies

Payments after 3 jobs = 64 pennies

To find the number of pennies you will receive after the 9th job.

Solution:

Let represent the payment after 1st job.

The sequence is in geometric sequence with common ratio = 4

The n term of a geometric sequence is given as:

For the sequence:

For the sequence we need the payment after 9th job. So, we are finding .

Thus, you will receive 262,144 pennies after completing the 9th job.

Answer 2

Given:

Friend pays 4 pennies for the first job and he quadruples the payment for each job completed.

To Find:

Find and solve the equation that finds the number of pennies you will get paid after the 9th dog grooming job.

Answer:

The number of pennies that he would pay after the 9th job is 262144.

Explanation:

We begin wwith the payment for 1 job which is 4 pennies.

We see that the payment for 2 jobs is quadrupled. Which means the payment comes out to be 4 x 4 = 16 pennies.

For the 3rd job, the payment is further quadrupled. So it is

4 x 4 x 4 = 16 x 4 = 64 pennies

We see that for each successive job, we must multiply by 4 to the payment for the previous job. In other words, for the 4th job, payment is

4 x 4 x 4 x 4 pennies,

for the 5th job, payment is

4 x 4 x 4 x 4 x 4 pennies

and so on.

So, for 'n' jobs, the payment will be 4 x 4 x 4 x ... x 4 (n times)

We can rewrite the above as the expression

`4^(n)`

Thus, the number of pennies paid for completing 'n' jobs, where n can be any natural number is

`4^(n)`

For the payment after the 9th job, n = 9. So,

`4^(n)=4^(9)=262144`

Therefore the number of pennies that he would pay after the 9th job is 262144.