The following graph shows the weight measurements of the ...
The following graph shows the weight measurements of the average infant from the time of birth
(t = 0) through age 2 (t = 24). By computing the slopes of the respective tangent lines, estimate the rate of change of the average infant's weight when t = 3 and when t = 18.
(Round your answers to one decimal place as needed.)
|t = 3 |1[pic] [pic][pic]lb/month |
|t = 18 |2[pic] [pic][pic]lb/month |
What is the average rate of change in the average infant's weight over the first year of life?
3[pic] [pic][pic]lb/month
[pic]
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2
Let f be defined as follows.
[pic][pic]
(a) Find the average rate of change of y with respect to x in the following intervals.
|from x = 6 to x = 7 |1[pic] |
| |[pic][pic] |
|from x = 6 to x = 6.5 |2[pic] |
| |[pic][pic] |
|from x = 6 to x = 6.1 |3[pic] |
| |[pic][pic] |
(b) Find the (instantaneous) rate of change of y at x = 6.
4[pic]
–––––––––––––––––––––––––––––––––––––––––––––––––––––––
The demand for Sportsman 5 X 7 tents is given by the following function where p is measured in dollars and x is measured in units of a thousand. (Round your answers to three decimal places.)
p = f(x) = −0.1x2 − x + 40
(a) Find the average rate of change in the unit price of a tent if the quantity demanded is between the following intervals.
|between 4400 and 4450 tents |$ 1[pic] [pic][pic]per 1000 tents |
|between 4400 and 4410 tents |$ 2[pic] [pic][pic]per 1000 tents |
(b) What is the rate of change of the unit price if the quantity demanded is 4400?
$ 3[pic] [pic][pic]per 1000 tents
–––––––––––––––––––––––––––––––––––––––––––––––––––––––
Under a set of controlled laboratory conditions, the size of the population of a certain bacteria culture at time t (in minutes) is described by the following function.
[pic][pic]
Find the rate of population growth at t = 11 min.
1[pic] [pic][pic]bacteria per minute
The position function of an object moving along a straight line is given by
s = f(t).
The average velocity of the object over the time interval [a, b] is the average rate of change of f over [a, b]; its (instantaneous) velocity at t = a is the rate of change of f at a.
A ball is thrown straight up with an initial velocity of 144 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 144t − 16t2.
(a) What is the average velocity of the ball over the following time intervals?
|[4,5] |1[pic] [pic][pic]ft/sec |
|[4,4.5] |2[pic] [pic][pic]ft/sec |
|[4,4.1] |3[pic] [pic][pic]ft/sec |
(b) What is the instantaneous velocity at time t = 4?
4[pic] [pic][pic]ft/sec
(c) What is the instantaneous velocity at time t = 8?
5[pic] [pic][pic]ft/sec
Is the ball rising or falling at this time? [pic]
[pic]rising [pic]falling
[pic][pic]
(d) When will the ball hit the ground?
t = 7[pic] [pic][pic]sec
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