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

1. ## Please - Need help tonight on a couple more calc problems

thanks

2. 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,
$\displaystyle 5(x^3+3)=5x^3+15$

3. thanks for the quick answer

4. 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,
$\displaystyle A(t)=100(.83)^t$

For the second part you need to find,
$\displaystyle 100(.83)^3\approx 57.18$

5. 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:

$\displaystyle f(t)=-16t^2+96t+6=0$

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:

$\displaystyle -0.06186, 6.06186$

So the ball is in the air $\displaystyle \approx 6.06$seconds.

b) The maximum height is achieved when $\displaystyle f(x)$ is
a maximum. As this is a quadratic we know this occurs midway
between the roots, so it occurs at $\displaystyle (-0.06186+6.06186)/2=3$,
so the maximum height is:

$\displaystyle f(3)=16\ 3^2+96\ 3+6=438$ feet.

c) Already answered at $\displaystyle t=3$seconds.

RonL