SOLUTION: Please help me solve this problem: Dr. Jane is studying the growing population of a species of jellyfish in a body of water. Each year, she records the population of jellyfish. Th

Question 1042512: Please help me solve this problem:
Dr. Jane is studying the growing population of a species of jellyfish in a body of water. Each year, she records the population of jellyfish. The first year, she recorded a population of 17 jellyfish. Every following year, the population increased by four times the previous year�s population. At this rate, what will be the jellyfish population in the 9th year of her study?
A. 1,485,477
B. 5,941,925
C. 371,371
D. 371,365
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i couldn't find any answer that was one of your selections.
in year 1, she has 17.
in year 2, she has 17 + 4 * 17 = 5 * 17 = 85
in year 3, she has 85 + 4 * 85 = 5 * 85 = 425
carry this out to year 9 and she has 17 * 5^8 = 6640625.

the key phrase in the problem statement is:
increased by four times the previous year�s population.

that means you take the current year's population and multiply it by 4 and then add it to the current year's population to get the next year's population.

if x in the first year, then it would be x + 4*x in the second year.
x + 4*x is equal to 5*x.

you wind up with a geometric progression where A9 = 17 * 5^8 = 6640625.

the general form of a geometric progression is An = A1 * r^(n-1).

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