the population P?

Question

the population P of a certain culture is expected to be given by a model P=100e^(rt) where r is a constant to be determined and t is a number of days since the original population of 100 was established. Find the value of r if the population is expected to reach 200 in 3 days.

Answer 1

P = 200
t = 3

Plug in your values:
200 = 100 e^(3r)

Divide both sides by 100:
e^(3r) = 200 / 100
e^(3r) = 2

Take the natural log of both sides:
3r = ln(2)

Divide both sides by 3:
r = ln(2) / 3

r ≈ 0.23104906

Double-checking:
P = 100 * e^(3 * 0.23104906)
P = 100 * 2
P = 200

Answer 2

Plug in the known values

200 = 100 e^(3t)

divide by 100: 2 = e^(3t)

Take natural log of both sides, the inverse of e: ln(2)= ln(e^3t)

On the right ln "cancels" e so ln(2) = 3t

Divide both sides by 3 and get t; you'll need a calculator to
find ln(2)

Answer 3

P=100e^(rt)
200 = 100e^(3r)
e^(3r) = 2
3r = ln2
r ≈0.230105