contestada

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.

Relax

Respuesta :

carlosego

For this case we have the following function:

[tex]S (t) = 3405.120e^{0.284t}[/tex]

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

[tex]Avr =\frac{S(t2) -S(t1)}{t2-t1}[/tex]

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

For the year 2001 [tex]t1 = 1[/tex]

For the year 2010 [tex]t2 = 10[/tex]

On the other hand:

[tex]S (t2) = 3405.120e^{0.284*10}\\S (t2) = 3405.120e^{2.84}\\S (t2) = 58281[/tex]

While:

[tex]S (t1) = 3405.120e^{0.284*1}\\ S (t1) = 3405.120e^{0.284}\\S (t1) = 4524[/tex]

So, we have to:

[tex]Avr =\frac{58281-4524}{10-1}[/tex]


[tex]Avr =\frac{53757}{9}\\Avr = 5973[/tex]

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

Answer:

[tex]Avr =5973\frac{millions-of-dollars}{year}[/tex]


Otras preguntas