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- anonymous

Deepak bought a new car at the dealership for $25,000. It is estimated that the value of the car will decrease 9% each year. Which exponential function models the value v of the car after t years?

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- anonymous

- schrodinger

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- anonymous

- Hero

Says "which" meaning, a list of answer choices are available to choose from.

- anonymous

a) v=25,000(1.9)^t
b) (same^^) (0.1)^t
c) (same^^) (0.91)^t
d) (same^^) (1.09)^t

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- anonymous

i know its either a or d because the 1 comes before the decimal, but i got confused because i don't remember if the 9 has a 0 infront or not

- Hero

It's not proper to post answer choices in that manner.

- Hero

How do you figure that it's either a or d?

- Hero

Explain how you eliminated b or c.

- anonymous

a) v=25,000(1.9)^t
b) v=25,000(0.1)^t
c) v=25,000(0.91)^t
d) v=25,000(1.09)^t
my b

- anonymous

i remember that the 1 comes before the decimal

- Hero

1 comes before the decimal for exponential INCREASE.

- anonymous

oh. so when it's not increasing, the 1 comes after the decimal?

- anonymous

? @Hero

- Hero

Basically, the only the only value of interest for the general formula \(v = 25000^{kt}\) is the k value. If there's an exponential increase, then \(k = 1 + r\) . If there's an exponential decrease, then \(k = 1 - r\) In this case \(r = 0.09\).

- anonymous

so it's (0.91)^t

- anonymous

- anonymous

- Hero

The general formula is \(v = 25000k^t\) sorry.

- mathstudent55

The formula for exponential growth or decay is:
F = P(1 + r)^t
where F = future amount
P = present amount
r = rate of growth or decay
t = number of years
If r is a rate of growth, r is positive.
If r is a rate of decay, r is negative.
You have a rate of decay, so r = -9% = -0.09
\(F = 25,000(1 - 0.9)^t\)
\(F = 25,000(0.91)^t\)

- anonymous

perfect! thank you!

- mathstudent55

Yw

- Hero

I wrote the k as an exponent. Sorry about that.

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