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.
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
[tex]4^{n}[/tex]
Thus, the number of pennies paid for completing 'n' jobs, where n can be any natural number is
[tex]4^{n}[/tex]
For the payment after the 9th job, n = 9. So,
[tex]4^{n}=4^{9}=262144[/tex]
Therefore the number of pennies that he would pay after the 9th job is 262144.
