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2 years ago

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Biologists stocked a lake with 160 fish and estimated the carrying capacity (the maximal population for the fish of that species

in that lake) to be 4,000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years. (b) How long will it take for the population to increase to 2000 (half of the carrying capacity)?

1 answer:

nignag [31]2 years ago

4 0

Answer:

The equation to find the number of fish after t years where y is the number of fish is:

y(t) = 160×3^(t) ( t <= 2.93 assuming that the maximum number of fish is 4000 )

Therefore when y(t) = 2000 2000 = 160×3^(t)

3^(t) = 25/2 log 3 (3^(t)) = log 3 (25/2) t = 2.29 years.

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2 years ago

21. Randy owns a computer store. In 1990, he sold 150 monitors. In 2000, he sold 900

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Answer:

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$x$ is the number of years since 1990.

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Thus, the two points are $(0,150)$ and $(10,900)$ .

The slope of a line with points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is given as:

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For the points $(0,150)$ and $(10,900)$ , the slope is given as:

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So, the y-intercept is 150.

Equation of a line in slope-intercept form is given as:

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Where, $m$ is the slope and $b$ is the y intercept.

Here, $m=75$ and $b=150$ .

Therefore, the equation that represents the above data is given as:

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