Thread: Please - Need help tonight on a couple more calc problems

thanks

Originally Posted by JohnSena

1. Write an equation for the graph obtained by shifting the graph of y=x^3 vertically upward by 3 units, followed by vertically sketching the graph by a factor of 5.

I guess,

thanks for the quick answer

Originally Posted by JohnSena

4. A standard cup of coffee contains about 100mg of caggeine, and caffeine leaves the body at a rate of about 17% per hour. Give a formula for the amount of caffeine in the body after t hours. How much caffeine is left in the body after 3 hours?

This is an exponential problem since you remove 17% it is the same as saying 83% of the total amount thus,


For the second part you need to find,

Originally Posted by JohnSena

2. A ball is thrown into the air at time t=0, and its height above ground (in feet) t seconds after it is thrown is given by f(t)=-16t^2+96t+6
a) How long is it in the air?
b) How high does it go?
c) When does it reach its maximum height?

a) the ball hits the ground when:



This will have two roots, one positive and the other negative, the
negative root is unphysical but the positive one is what you want.

The roots are:



So the ball is in the air seconds.

b) The maximum height is achieved when is
a maximum. As this is a quadratic we know this occurs midway
between the roots, so it occurs at ,
so the maximum height is:

feet.

c) Already answered at seconds.

RonL