The weight, W, in lbs, of a child is a function of its age, a, in years, so W = f(a). (a) Do you expect f ′(a) to be positive or negative? Why? (b) What does f(8) = 45 tell you? Give units for the numbers 8 and 45. (c) What are the units of f ′(a)? Explain what f ′(a) tells you in terms of age and weight. (d) What does f ′(8) = 4 tell you about age and weight? (e) As a increases, do you expect f ′(a) to increase or decrease? Explain.

a) positive

b) the child is 45 lbs when she's 8 years old

c) lbs/year

d) The child increases 4 lbs/year when she's 8 years old

e) decrease

Step-by-step explanation:

a) Positive for the child because as they grow (age increases), a normal child should gain weight.

b) It tells that when age (years) = 8, the child weights 45 lbs

c) The unit of f' would be lbs/year. As it's a derivative of f (lbs) with respect to time t (years)

d) f'(8) = 4 tells us that the child weights increase at the rate of 4 lbs/year when she's 8 years old

e) As a increases f'(a) would decreases, as the rate of weight gain of a child would be slowing down as she grows.

→

3.2 liters of lemonade were consumed during the party.

→Step-by-step explanation:

What we know

Well there is 2,500 mL of strawberry lemonade

There are  2 liters of cherry

There are 5 deciliters of dog limeade

So the 5 deciliters of dog limeade doesn't count because it is limeade, not lemonade.

The question is asking for the number of liters so we need to convert the 2,500 milliliters of lemonade to liters.

Which will be 2.5 liters of lemonade.

There are also 2 liters of cherry lemonade so 2.5 + 2 is 4.5.

So if 1.3 liters were left over doing 4.5 - 1.3 we get 3.2, meaning 3.2 liters of lemonade were consumed during the party.