Maths help?

a) Since you are multiplying each hour by an additional 1.15, it increases in population by 15% every hour.

b) your answer of 3,000 is correct.

c) your answer is not correct. What's the size after 24 hours, plug in 24 for t and solve for P:

P = 3000 * 1.15^24

P = 3000 * 28.6252

P = 85875.529

Since you wouldn't have half a bacteria, you could round down:

85,875

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p is proportional to the square of e.

Using "k" as a constant, if p is proportional to the square of e, the equation is:

p = ke²

When e = 5 and P = 300, you can find your constant:

300 = k(5)²

300 = 25k

k = 12

Now we have plug in the value "k" into the equation and we have the answer to part a:

p = 12e²

Part b: what is P when e = 3.5? plug in this value for e and solve:

p = 12(3.5)²

p = 12 * 12.25

p = 147

part c: what is e when P = 507?

507 = 12e²

169/4 = e²

e = 13/2 (you'd throw out the negative value since you're talking about a physical spring)

a) 100 * (1.15 - 1) = 100 * 0.15 = 15

b) 3000 * 1.15^0 = 3000 * 1 = 3000

c) 3000 * 1.15^24 =~ 85875.528573364372871547774721928