need help w/ rate of change of P(t) = 1000t/t + 10, t>=10

[Rebel*and*Saint]

Suppose that P(t) = 1000t/t + 10 represents the population of a certain kind of bacteria at time t, where t > 10.

a) What is the rate of change of the bacteria population? Is the population growing or decreasing?

Thanks for any help

 

[stapel]

I will guess that you mean the function to be as follows:

. . . . .\(\displaystyle \L P(t)\, =\, \frac{1000t}{t\,+\,10}\)

...for t > 10. (As posted, the function simplifies to 10010, which doesn't make much sense.)

Since P(t) represents the population P at time t, then the rate of change in the population would be given by the derivative. So differentiate P(t) to find the formula for the rate of change.

Evaluate the sign of the derivative to determine if the rate of growth is positive (so the population is growing) or negative (so the population is decreasing).

If you get stuck, please reply showing all of your steps and reasoning. Thank you.

Eliz.