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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

Elijah Allen

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

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]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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!?

in the form y = y0e^kt

Help!?