Question

Suppose an experimental population of amoeba increases according to the law of exponential growth. There were 100 amoeba after the second day of the experiment and 300 amoeba after the fourth day. Approximately how many amoeba were in the original sample?(see attachment)

Answer 1

the equation for exponential growth is

P=Ae^(rt)

where
r=rate (percentage divided by 100)
t = time
A = initial size of sample
P = size of sample after growth

Answer 2

so in 2 days

we have that

t = 2 days
A = 100
r = ?
P = 400

Answer 3

solve for r using logarithms, then solve for the initial population by solving for A and setting 100 to p and time to 2 days as there were a 100 amoeba after 2 days

Answer 4

P=Ae^(rt)
so for the first part

400 = 100e^(r2)
400/100 = e^(r2)
ln(400/100) = ln(e^(r2))
ln(400/100) = (2r)ln(e)
ln(400/100) = 2r(1)
ln(400/100)/2 = r