Your friend asks you to him with his dog grooming business and will pay you 4 pennies for the first job. you agree to 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.

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.

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

Step-by-step 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

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

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

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

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