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.