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Rudiy27
3 years ago
13

A new species of fish is released into a lake, and the fish multiply quickly. The growth of their population is modeled by the e

xponential function P(t) = 7bt, where t is the time in weeks after the release and b is a positive unknown base. After observing the population growth over a few weeks, the exponential function P(t) = 7(2)t is used to model the growth. Interpret the significance of 2 in the function as it applies to the situation.
A) the population is doubling each week

B) the population is doubling each month

C) the population is counted every 2 weeks

D) the population is increasing by 2 fish each week
Mathematics
1 answer:
Rainbow [258]3 years ago
5 0

Answer:

The answer is A

Step-by-step explanation:

So b is equal to a positive unknown base. With the other variables as unknown the first week is equal to 7, and the next week is equal to 14, and as t increases, so will the population.

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Given that r=\theta, then r'=1

The slope of a tangent line in the polar coordinate is given by:

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m= \frac{\sin\theta+\theta\cos\theta}{\cos\theta-\theta\sin\theta}



Part A:

For horizontal tangent lines, m = 0.

Thus, we have:

\sin\theta+\theta\cos\theta=0 \\  \\ \theta\cos\theta=-\sin\theta \\  \\ \theta=- \frac{\sin\theta}{\cos\theta} =-\tan\theta

Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:

</span><span>θ = 0

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\cos\theta-\theta\sin\theta=0 \\  \\ \Rightarrow\theta\sin\theta=\cos\theta \\  \\ \Rightarrow\theta= \frac{\cos\theta}{\sin\theta} =\sec\theta

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Answer:

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