Not sure what to do (rate of change of % of public aware)

[stackey82]

I have a problem that I believe I got but want to make sure. The question follows-

The awareness of the product is appx. by A(t)= (10t^2)(2^-t), where t is the time in months. Find the rate of change of the percent of public that is aware of the product after 5 months.

I used the product rule but not sure if I applied it properly
(20t)(2^-t)+(10t^2)(2t^(-t-1))
Then combine and this is where i think i messed up
((20t)/(2^t))+((10t^2)/(2t^(t+1))
Then I plugged in the 5 for t and got 3.3125 but this doesn't seem right to me. If I am right great if not can someone show me where I went wrong? Thanks and it would be greatly appreciated.

[stapel_eliz]

The awareness of the product is appx. by A(t)= (10t^2)(2^-t), where t is the time in months. Find the rate of change of the percent of public that is aware of the product after 5 months.

I used the product rule but not sure if I applied it properly
(20t)(2^-t)+(10t^2)(2t^(-t-1))

You're find on the derivative of the 10t² part, but you might want to review the rules for exponentials. They are not the same as polynomials!

In general, for f(x) = a^x, the derivative is f'(x) = a^x ln(a), where "ln(a)" is the natural logarithm of "a".

In your case, a = 2.

[stackey82]

Original problem (10t^2)(2^-t)

So I would get
(20t)(2^-t)+(ln2)(2^-t)(-1)(10t^2) with t=5

3.125+(-5.415)= -2.29

[stapel_eliz]

I get the same result. Good work!