Question

the annual sale (in millions of dollars) at Apple from 2001 through 2010 can be modeled by S(t)=3405.120e^0.284t. Where t is the number of years since 2000. What is the units for the average rate of change of sales with respect to time over the period from 2001 to 2010.

Answer 1

For this case we have the following function:

`S (t) = 3405.120e^(0.284t)`

By definition, the average rate of change is given by:

`Avr =(S(t2) -S(t1))/(t2-t1)`

If t is the number of years since 2000, we have to:

For the year 2001
`t1 = 1`

For the year 2010
`t2 = 10`

On the other hand:

`S (t2) = 3405.120e^(0.284*10)\\S (t2) = 3405.120e^(2.84)\\S (t2) = 58281`

While:

`S (t1) = 3405.120e^(0.284*1)\\ S (t1) = 3405.120e^(0.284)\\S (t1) = 4524`

So, we have to:

`Avr =(58281-4524)/(10-1)`

`Avr =(53757)/(9)\\Avr = 5973`

So, the average rate of change is given by: 5973

Answer:

`Avr =5973(millions-of-dollars)/(year)`