Marginal Cost Fcn MC=20 +68^(-.01q): find total cost

[KLS2111]

I am trying to help my friend with Calc and I have not taken it in about 4 years, so I am struggling with the following problem.

The Marginal cost function is given by MC=20 +68^(-.01q) , where q is the quantity produced. If C(0)=2000, find the total cost to the nearest hundred dollars of producing 100 units.

I recall that MC is the deriv of the cost function, so I believe that I need to integrate the function. I think I am integrating e wrong because I am coming up with 20q - 6800e^(-.01q) +2000. When I then plug in 100 for q... my answer is unreasonable.

Thanks for any help you can give me!

 

[skeeter]

for base a > 0, the antiderivative of \(\displaystyle \L a^{kx}\) is \(\displaystyle \L \frac{a^{kx}}{k \cdot \ln{a}}\)

 

[KLS2111]

Opps... On the MC function

I posted the original MC function wrong. It is really MC = 20 +68e^(-.01q)

I left the e out. If anyone could help me find teh antideriv of that I would appreciate it!

 

[skeeter]

the antiderivative of \(\displaystyle \L Ce^{kx}\) is \(\displaystyle \L \frac{Ce^{kx}}{k}\)