SOLUTION: Please help me solve this problem, I would really appreciate it if you would look over my answer and tell me whether I am right or wrong. The number of bacteria y after time t

Question 1015193: Please help me solve this problem, I would really appreciate it if you would look over my answer and tell me whether I am right or wrong.
The number of bacteria y after time t (in minutes) is given by y= 10000e^(-0.01t). At what rate is the population changing at t= 3 minutes? Express your answer to the nearest unit. Is this an example of natural growth or decay? Explain.
I took the first derivative and got:
y'(t)= 100e^(-0.01t)
Then plugged in 3 for t:
y'(3)= 100e^(-0.01(3))
And finally got:
y'(3)= 100e^(-0.03)
Is this right or wrong?
As for the explanation, I know that it's an example of exponential decay but I need help explaining why it is.
Thanks, your help is always appreciated!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Close, but you have a sign error.

Exponential decay is decreasing function. A function is decreasing in any interval where the first derivative is negative. The derivative of

is negative over the entire domain of the function whenever

John

My calculator said it, I believe it, that settles it

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