Question

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

Answer 1

add four and nine in the first to boxes and in the second column put 262144

Explanation:

Basically if you do 2 grooming jobs its four to the 2nd power. 3 grooming jobs would be 4 to the third power. 4 would be 4 to the fourth power and so on. If she does 9 grooming jobs it would be 4 to the 9th power. 4 to the 9th power would look like 4x4x4x4x4x4x4x4x4 which would equal 262,144.

Answer 2

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
`a_1` represent the payment after 1st job.

`a_1=4`

`a_2=16`

`a_3=64`

The sequence is in geometric sequence with common ratio = 4

The n
`th` term of a geometric sequence is given as:

`T_n=a_1r^((n-1))`

For the sequence:

`a_1=4`

`n=9`

`r=4`

For the sequence we need the payment after 9th job. So, we are finding
`T_9`.

`T_9=4(4)^((9-1))`

`T_9=4(4)^(8)`

`T_9=4(65536)`

`T_9=262144`

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