Question

Suppose that the rate of growth of a population of organisms is 5% of the number present, t being measured in days. If there are 10,000 individuals present initially, how many are present in 10 days? When will the initial population has doubled?

Answer 1

Answer:

i)16,289 organisms

ii)14.2067 days

Step-by-step explanation:

Population grows compounded.

The formula for CI is P(1+R/100)^T

i)

Amount=10k*(1+0.05)^10

According to PEMDAS rule, the exponents should be done first.

Amount=10,000*1.05^10

Amount~=10,000*1.62889

Amount~=16,289 organisms

ii)

Amount should be 20k

So,

20k=10k*(1+0.05)^n

1.05^n=2

n=log{1.05}2

n=log(2)/log(1.05)

n=14.2067 days

The population will cross the 20k mark after 15 days have passed.

Note: log{x}y means log(y) base x.

XYZk means XYZ thousands.

log{x}y=log{c}y/log{c}x this is a

general property for logs.

log(x) means log{10}x.