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# Derivatives and Rates of Change

1.A ball is thrown directly upward from the ground. Its height above the ground is given by

h=50t-5t2

Where h is measured in metres and t is measured in seconds. Determine

a)its initial velocity
b)the maximum height of the ball
c)when the velocity is negative
d)how long the ball is in the air
e)the velocity with which the ball strikes the ground

2.The population (P) of a bacteria culture is described by

P(t)=20t3+150t+1000

Where t is measured in hours. Calculate how many bacteria exist at t=10 hours, as well as the population's growth rate at that time.

#### Solution Preview

1.A ball is thrown directly upward from the ground. Its height above the ground is given by

h=50t-5t2

where h is measured in metres and t is measured in seconds. Determine

a)its initial velocity

h=50t-5t2
=> v = dh/dt = 50-10t
When t = 0, v = 50 ...

#### Solution Summary

Derivatives and rates of change are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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