Question

3) The population of a culture of cells after t days is approximated for the following function for 0 ? t ? 400. P(t) = 1500 / (1 + 5e^(-0.02t)) The graph of the population function is shown below. [a] (2 pts) What is the average growth rate within the first 100 days? [b] (3 pts) Differentiate the population function to find an expression for the growth rate P'(t). [c] (5 pts) Use any graphing utility to plot the graph of P'(t) on the interval [0, 400]. The utility GeoGebra, which is available for free download, is used to plot the above graph. Your graph should show both the axes and it should be clear. [d] (2 pt) From the graph of P'(t), find the approximate value of t when the growth rate is maximum. Call that value tmax. [e] (3 pts) With respect to the graph of P(t) shown above, what is (tmax, P(tmax)) called? Why? (Hint: Use your knowledge from section 4.5 of the textbook.)

          3) The population of a culture of cells after t days is approximated for the following function for 0 ? t ? 400.

P(t) = 1500 / (1 + 5e^(-0.02t))

The graph of the population function is shown below.

[a] (2 pts) What is the average growth rate within the first 100 days?
[b] (3 pts) Differentiate the population function to find an expression for the growth rate P'(t).
[c] (5 pts) Use any graphing utility to plot the graph of P'(t) on the interval [0, 400]. The utility GeoGebra, which is available for free download, is used to plot the above graph. Your graph should show both the axes and it should be clear.
[d] (2 pt) From the graph of P'(t), find the approximate value of t when the growth rate is maximum. Call that value tmax.
[e] (3 pts) With respect to the graph of P(t) shown above, what is (tmax, P(tmax)) called? Why? (Hint: Use your knowledge from section 4.5 of the textbook.)

3) The population of a culture of cells after t days is approximated for the following function for 0 ? t ? 400.

P(t) = 1500 / (1 + 5e^(-0.02t))

The graph of the population function is shown below.

[a] (2 pts) What is the average growth rate within the first 100 days?
[b] (3 pts) Differentiate the population function to find an expression for the growth rate P'(t).
[c] (5 pts) Use any graphing utility to plot the graph of P'(t) on the interval [0, 400]. The utility GeoGebra, which is available for free download, is used to plot the above graph. Your graph should show both the axes and it should be clear.
[d] (2 pt) From the graph of P'(t), find the approximate value of t when the growth rate is maximum. Call that value tmax.
[e] (3 pts) With respect to the graph of P(t) shown above, what is (tmax, P(tmax)) called? Why? (Hint: Use your knowledge from section 4.5 of the textbook.)

Added by Kelly R.

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