Question 1015308
the population of grasshoppers quadruples in 20 days.


the present population is 40 million.


what will it be in 50 days.


exponential growth formula is f = p * e^(kt).


f is the future population.
p is the present population.
k is the growth per unit time.
t is the amount of time.


the population quadruples every 20 days.


you can solve for k in the following manner.


f = 4
p = 1
t = 20


this formula tells you that your current population is quadrupling in 20 days and it is solving for the growth rate per day.


f = p * e^(kt) becomes 4 = 1 * e^(20k)


this is the same as 4 = e^(20k)


take the natural log of both sides of this equation to get ln(4) = ln(e^(20k))


since ln(e^(20k)) = 20k*ln(e) and since ln(e) = 1, then 20k*ln(e) = 20k.


your formula of ln(4) = ln(e^(20k)) becomes ln(4) = 20k.


divide both sides of this equation by 20 to get ln(4)/20 = k.


solve for k to get k = .0693147181.


k is your daily growth rate.


now that you know the value of k, go back to the original formula of f = p * e^(kt) and replace p with 40 and k with .0693147181 and t with 50 to get:


f = 40 * e^(.0693147181 * 50)


40 is the current population.
.0693147181 is the daily growth rate.
50 is the number of days.


solve for f to get f = 1280 million.


that's the population in 50 days.