Question

The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.

V(t) = 29,900(0.80^t)

Find the initial value of the car and the value after 12 years. Round your answers to the nearest dollar as necessary.

Initial value:
Value after 12 years:

Answer 1

for initial valve put t=0 in eq and for 12 years put t=12 in eq.

Answer 2

can you walk me through solving? I am having some trouble with this

Answer 3

What is problem?

Answer 4

I am having trouble solving it

Answer 5

for initial value t=0 ,v(0)=29,900(0.80^0)
and a^0=1 where a is any numbers use this

Answer 6

V(t) = 29,900(0.80^t) is an EXPONENTIAL FUNCTION. 0.80 is the BASE of this exponential function, and t is the EXPONENT or POWER to which this base is raised.

Either using your calculator or by and, evaluate 0.80^0, 0.80^2, 0.80^3, and so on.

Now put your exponential function to use: If you substitute 12 for t, V(t) = 29,900(0.80^t) will give you the (depreciated) value of the car after 12 years.

Please show your work. Thanks.

Answer 7

What kind of calculator have you?

Answer 8

I have a scientific calculator

Answer 9

@mathmale

Answer 10

Have you done exponentiation on your calculator before? Try 2^3. Answer should be 8.

Try 5^2. Answer should be 25.

Answer 11

Yes it works!

Answer 12

Then evaluate 0.8^0, 0.8^1, 0.8^2, and so on.

Answer 13

What is 0.8^2?

Answer 14

0.64

Answer 15

Right!

So, you want to calculate the value of the car after 12 years.

The pertinent function is V(t) = 29,900(0.80^t).

Find V(12). To do this, calculate 0.8^12 first, and only then multiply that result by $29,900. V(12)=?

Answer 16

this follows "order of operations" rules.

Answer 17

So the answer would be 1,992.864825?

Answer 18

And if I round that to the nearest dollar it would be 1,993?

Answer 19

wrong calculation

Answer 20

No sorry it would be 2054.712354. I put 29,000 on accident

Answer 21

So the answer would be 2055?

Answer 22

2055 what?

Answer 23

$2,055 is the value after 12 years

Answer 24

Cool. Perfect! Nice work! Happy New Year!

Answer 25

Have to get off the 'Net now, but hope to be able to work with you again.

Answer 26

Ok thanks!

Answer 27

Sure! Bye.