Question

The eating behavior of a typical human during a meal can be described by

I(t)=27+72t-1.5t^2 ,

Where t is the number of minutes since the meal began and I(t) represents the amount (in grams) that the person has eaten at time t.

a.Find the rate of change of the intake of food for a person 5 minutes into a meal, and interpret it.

Answer 1

Well the rate of change is the speed, so to find the speed take the first derivative of the function which is 3t-72.

Answer 2

so i need to put 5 in the fuction right?

Answer 3

Yes lol.

Answer 4

Sorry the function is -3t+72. Because time cannot be negative.

Answer 5

the next questions to this questions are
b) Verify that the rate at which food is consumed is zero 24 minutes after the meal starts.
c) Comment on the assumptions and usefulness of this function after 24 minutes. On the basis of your answer, determine a logical range for the function

Answer 6

yeah i realised that..dont worry

Answer 7

with b i was finking i jux neeed to put 24 in the function which would be =0

Answer 8

but i dont know how to explain c

Answer 9

can you help ?

Answer 10

Yes

Answer 11

ok please help me with the explanation then

Answer 12

b. Substitute 24 into -3t+72, that would be zero!

Answer 13

no i mean c

Answer 14

I'm calculating the range.

Answer 15

ok

Answer 16

What you will do is to get the vertex of that function.

Answer 17

how do i do that?lol

Answer 18

Use the formula