precalc question

Question

A ship embarked on a long voyage. At the start of the voyage, there were 500 ants in the cargo hold of the ship. One week into the voyage, there were 800 ants. Suppose the population of ants is an exponential function of time.

(a) How long did it take the population to double?

(b) How long did it take the population to triple?

(c) When were there be 10,000 ants on board?

(d) There also was an exponentially-growing population of anteaters on board. At the start of the voyage there were 17 anteaters, and the population of anteaters doubled every 2.8 weeks. How long into the voyage were there 200 ants per anteater?

Answer 1

I have provided a start for a, b, and c.

anteaters: 17(2)^t/2.8

200 ants per anteater:(200)(17)(2)^t/2.8

number of ants: 500e^0.47t

(200)(7)(2)^t/2.8 = 500e^0.47t

Can you solve for t and answer?

Answer 2

"exponential function of time" : y = f(x) = m*k^x

Based on the given data, we can write 800 = 500*k¹

So k = 1.6

To double: 1000/500 = 2 = 1.6^t

log 2 = t * log 1.6

t = log 2 / log 1.6 = 1.48 weeks

To triple:

3 = 1.6^t

t = 2.34 weeks

To get to 10,000:

ratio is 10,000/500 = 20

20 = 1.6^t

t = 6.38 weeks