Your friend asks you to help her babysit and will pay you 3 pennies for the first job. You agree to help if she triples your payment for each job completed. After 2 jobs, you will receive 9 pennies, and after 3 babysitting jobs, you will receive 27 pennies.
Complete and solve the equation that finds the number of pennies she will pay you after the 9th babysitting job.
= number of pennies for 9th babysitting job
Payment for the 9th babysitting job =
pennies
3^9 = 19683
Thank you! Have a nice day! :)
To find the number of pennies your friend will pay you after the 9th babysitting job, we need to determine the pattern of payment increase.
We know that for each job completed, your friend triples your payment. Let's analyze the given information:
1st job: 3 pennies
2nd job: 9 pennies (3 pennies * 3)
3rd job: 27 pennies (9 pennies * 3)
From the given data, we can observe that the payment for each job is obtained by multiplying the previous payment by 3. Therefore, we have a geometric sequence with a common ratio of 3.
To find the payment for the 9th babysitting job, we can use the formula for the nth term of a geometric sequence:
an = a * r^(n-1)
where:
an = nth term (payment for the 9th job in this case)
a = first term (3 pennies)
r = common ratio (3)
n = number of terms (9)
Using the formula, we can substitute the values:
payment for the 9th job = 3 * 3^(9-1)
payment for the 9th job = 3 * 3^8
payment for the 9th job = 3 * 6561
payment for the 9th job = 19683 pennies
Therefore, your friend will pay you 19683 pennies for the 9th babysitting job.