Growth population change

[Creager]

A hot, wet summer is causing a mosquito population explosion in a lake resort area. The number of mosquitos is increasing at an estimated rate of 2100+7e^(.07t) per week (where t is measured in weeks). By how much does the mosquito population increase between the 4th and 8th weeks of summer?

a.14,222 b.10,940 c.15,316 d.6,564 e.7,658

This seemed easy. Yet it is multiple choice and I am not getting the right answer....

pop = integral[4,8] (2100+7e^(.07t))

pop = [4,8] ( 2100t+(7/.07)e^(.07t) )

pop = (2100*8 + 100e^(.07*8))-(2100*4+100e^(.07*4)) = 8442.75

what am I doing wrong?

 

[fcabanski]

Are you certain it's e^(.07t)?

e^(.7t) results in answer b.

If it is .07t, none of the answer choices make sense. The compounding component is so small, that 2100 is by far the major component of the increase. In 4 weeks the increase would be around 8400. But none of the answer choices is around 8400. a,b, and c are too large. d and e are too small.

A hot, wet summer is causing a mosquito population explosion in a lake resort area. The number of mosquitos is increasing at an estimated rate of 2100+7e^(.07t) per week (where t is measured in weeks). By how much does the mosquito population increase between the 4th and 8th weeks of summer?

a.14,222 b.10,940 c.15,316 d.6,564 e.7,658

This seemed easy. Yet it is multiple choice and I am not getting the right answer....

pop = integral[4,8] (2100+7e^(.07t))

pop = [4,8] ( 2100t+(7/.07)e^(.07t) )

pop = (2100*8 + 100e^(.07*8))-(2100*4+100e^(.07*4)) = 8442.75

what am I doing wrong?

 

[Creager]

Are you certain it's e^(.07t)?

e^(.7t) results in answer b.

If it is .07t, none of the answer choices make sense. The compounding component is so small, that 2100 is by far the major component of the increase. In 4 weeks the increase would be around 8400. But none of the answer choices is around 8400. a,b, and c are too large. d and e are too small.

you're right... i thought i was right because my number was right in the middle, thanks anyways