Could you please clearly show all of your work and ALL the steps involved showin

Question

Could you please clearly show all of your work and ALL the steps involved showing how to get the answer. I will have to do a problem like this on my test tommorow

A zoologist is writing a dissertation on the impact of the fish population in Lake Maben since the Bellmore Company built a factory nearby. Initial sampling shows that the fish population can be modeled by p(t) 15 (0.6)e 0 s t s 10 where t represents the number of years since the factory opened, and p(t represents the fish population in hundreds. (a) Determine p (t p (t (b) Evaluate p (1). Round your answer to two decimal places p (1 Interpret p (1). yea after the factory opened, the fish population was decreasing at a rate of fish per year. compare p (1) to p (s) 5 years after the factory opened, the fish population was decreasing at a rate of fish per year, which Is Select the decay rate one year after the factory opened

Explanation / Answer

Given, P(t)=15*(0.6)^t

(a)P'(t)=d{P(t)}/dt=d{15*(0.6)^t}/dt=15*(0.6)^t*ln(0.6)=-7.66(0.6)^t

(b)P'(1)=-7.66(0.6)^1=-4.596

so, 1 year after the factory opened, the fish population was decreasing at a rate of 4.59*100=459 fish per year

P'(5)=-7.66*(0.6)^5=-0.596

so, 1 year after the factory opened, the fish population was decreasing at a rate of 0.59*100=59 fish per year

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