Question

5. The current population size for a termite colony is 153,986 termites. If the current per capita rate of increase is 0.273, by what percent is the termite colony growing?

Answer 1

Current population size = P° = 153,986

Population after growth at a time = P t = ?

Per capita rate of increase = rate = r = 0.273

Percent by which termite colony growing = ?

This is the information given in the question. To find the percent of growing termite colony, we will first find out the population after a time. Let time, t = 1 year.

This can be find out by using formula,

P t = P° * e ^r*t -------- a

P t = population after time, t

P° = initial population or current population

r = rate of growth

t = time

e = constant; euler number = 2.718

Putting all values in equation -------- a

P°= 153,986

r = 0.273

e = 2.718

t = 1

P t = 153,986 * 2.718 ^ 0.273*1

P t= 202,316.516

​​​​​​Or P t = 202,317 (approx)

to find percent change in population, we use formula

% = ( Pt - P°) / P° * 100

% = (202,317 - 153,986) / 153,986 *100

% = 48331 * 100 / 153,986

= 4833100 / 153,986

= 31.386

or 31.39 % ( approx)

it is for 1 year or time, t =1.

if time is >1 then calculated% is divided by the time period.

thank you....

​​​​​​​expect a ?? ?....