Need help asap! Thank you

Question

2. A potato was launched in the air using a potato gun. The function for the situation was h(t) = -16t² + 100t + 10, where t was the time in seconds and h(t) was the height in feet.

a. What was the maximum height of the potato?

b. What was the lowest height of the potato?

c. What was the lowest time that applies to the actual situation?

d. What is the greatest time that applied to the actual situation?

e. Using your answers to parts a through d, what are the domain and range of the function, as they apply

to this situation? Use set builder notation.

Answer 1

h(t) =-16t^2 + 100t + 10

take the derivative and set equal to zero

h'(t) = -32t +100 = 0

t= 100/32 = 25/8 = 3.125 seconds to reach maximum height

h(25/8) = -16(25/8)^2 +100(25/8) + 10 = max height

=-156.25 + 312.5 + 10 = 322.5-156.25 = 166.25 feet

eventually the potato hits the ground reaching a lowest height of 0 feet

that occurs when h(t) = 0 = -16t^2 +100t +10

8t^2 -50t -5 = 0

t = 50/16 + (1/16)sqr(50^2 +160) = 25/8 + (1/16)sqr(2660) = about 6.35 seconds

a little more than twice the time to reach a maximum height

domain is 0 < t < 6.35 seconds

range is 0 < t < 166.25 feet