Question

A population of grasshoppers quadruples in twenty days. Assuming exponential growth, if the present population is 40 million, what will it be in 50 days? Answer the question by first finding the number y of grasshoppers as a function of time t (in days)?

in the form y = y0e^kt

Help!?

Answer 1

The grashopper population after `50` days will be `1280` million.

Explanation:

The exponentia growth formula is `y_t= y_i*e^(kt) ; y_i and y_t`

are the initial population and population at time `t` respectively

and `k` is % of rate of growth. The grasshoppers quadruples

in `20` days `y_i=40`million then `y_t=160` million

`:. 160= 40 *e^(k*20) or e ^(k*20)= 4`. Taking natural log in both

sides we get `20k = ln (4) or k = ln(4)/20= 0.069315`

The population after `50` days will be `y_t= y_i*e^(kt)` or

`y_50= 40*e^(0.069315*50) = 1280` million.

The grashopper population after `50` days will be `1280`million. [Ans]