Rhonda started a business. Her business made $30,000 in profits the first year. Her annual profits have increased by an average of 5% each year since then.

(a) Write an explicit rule to model the sequence formed by the profits of Rhonda's business each year. Use the formula an=a1 (r) n-1. (Hint: increase means to add 1 to your %)

(b) Use the rule to determine what the annual profits of Rhonda's business can be predicted to be 15 years from the start of her business. Round your answer to the nearest dollar. Do not round until the end. Show your work.

Question

Mathematics

Markus Newman

29 August, 12:57

Rhonda started a business. Her business made $30,000 in profits the first year. Her annual profits have increased by an average of 5% each year since then.

(a) Write an explicit rule to model the sequence formed by the profits of Rhonda's business each year. Use the formula an=a1 (r) n-1. (Hint: increase means to add 1 to your %)

(b) Use the rule to determine what the annual profits of Rhonda's business can be predicted to be 15 years from the start of her business. Round your answer to the nearest dollar. Do not round until the end. Show your work.

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Answers (1)

Know the Answer?

Alisha Snow · Answer 1

an = 30000 (1.05) ^ (n-1)

a15 = 59398

Step-by-step explanation:

a) a1 = 30000

r = 1.05

an=a1 (r) ^ (n-1)

an = 30000 (1.05) ^ (n-1)

b) a15 = 30000 (1.05) ^ (15-1)

a15 = 30000 (1.05) ^14

a15 = 30000 (1.979931599)

a15=59397.94798

a15 = 59397.95

to the nearest dollar

a15 = 59398