C(t) = 0.01(0.2t2 + 4t + 64)2/3

Question

(a) Find the rate C '(t) at which the level of CO is changing with respect to time t.

(b) Find the rate at which the level of CO will be changing 7 yr from now. (Round your answer to four decimal places.)

Answer 1

It is a little hard to tell what the equation is, in general if you want to write equations like this in text use the _subscript or ^superscript formats or if they are not available use the up carat ^ (shift+6) for exponents.

As this looks like a homework question, I won't directly provide an answer, but I can provide some guidance.

Assuming the equation actually reads: 0.1 (0.2t² + 4t + 64)^2/3 then one thing that might help you apply all the appropriate rules is remembering how to deal with exponents. The 2/3rds exponent can be split into a 1/3 and a 2. So 0.1 ( (blahblah)^2 )^1/3.

Then use the chain rule, which states that if you want the derivative of a complicated nested thing like this, take the derivative of the outermost part as if it were it's own thing. So, what is d/dx of x^1/3?

Then multiply it by the derivative of the thing inside that set of parentheses. And so forth until you've taken the derivative at each level.