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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 n(t) = 2100 + 10e0.9t per week (where t is measured in weeks). By how much does the mosquito population increase between the fifth and ninth weeks of summer? (Round your answer to three decimal places.) mosquitos

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Answer:

[tex]n(4)=2465.982[/tex]

Step-by-step explanation:

we have that [tex]n(t)=2100+10e^{0.9t}[/tex] where t is measured in weeks and n(t) number of mosquitos

Find n(t) to t=4 (9tn week - 5th week = 4 weeks)

[tex]n(4)=2100+10e^{0.9*4} =2100+10e^{3.6}=2100+10*36.598243=2100+365.98243\\n(4)=2465.982[/tex]