Your friend asks you to cut grass this summer and will pay you 2 pennies for the first job. you agree to if he doubles your payment for each job completed. after 2 lawns, you will receive 4 pennies, and after 3 lawns, you will receive 8 pennies. complete and solve the equation that finds the number of pennies he will pay you after cutting the 15th lawn.

Step-by-step explanation:

We are given that your friend asks you to help cut the grass this summer and will pay you 2 pennies for the first job

We are given that you are agreed to help if doubles your payment for each job completed.

After 2 lawns, you will receive money= 4 pennies

After 3 lawns, you will receive money=8 pennies

Let total earn pennies are for lawn n and be the number of pennies receive after first job completed.

We have to prove that

It is proved by induction method

Hence, is true for n=1

Let   is true for n=k

Now, we shall prove that for n=k+1 is true

Substitute n=k+1 then we get

Hence, it is true for n=k+1

Hence, proved.

Now substitute n=15 then we get

Hence, the number of pennies he will pay you after cutting the 15th lawn=32768.