Question

The equation, y = 10(1.0605)x, represents the winning prize money, in thousands, for first place in the Indianapolis 500 auto race. x represents the number of years after 1911, the first year.

What is the value for 1911 (x = 0)? This is the prize money, in thousands. For instance, if you got 23, this represents $23,000.

A. $10,605
B. $10,000
C. $0

Wouldnt the correct answer be A?

Answer 1

I have to assume that you mean \[y = 10(1.0605)^x\]

Answer 2

Yes sorry about that.

Answer 3

If that is correct then let me ask you.. What is \(5^1\)

Answer 4

5

Answer 5

What is \(5^0\)

Answer 6

Ohhhhh then it would be nothing

Answer 7

No

Answer 8

What is \(5^2\)

Answer 9

25

Answer 10

and \(5^3\)

Answer 11

125

Answer 12

Ok, so lets look at it going backward:

\[5^3 = 125\]
\[5^2 = 25 = \frac{125}{5}\]
\[5^1 = 5 = \frac{25}{5}\]
\[5^0 =\ ? = \frac{5}{5}\]

Answer 13

So what is \(5^0\)

Answer 14

Then it would be... i think 1?

Answer 15

Right

Answer 16

nicely done!

Answer 17

And this is the case for any number:

\[b^0 = \frac{b}{b} = 1, \forall b \ne 0\]

Answer 18

Ohhh.... Yea makes much more sense. I am so thankful for this cite!!!! My dad doesnt remember much from high school. :P So he often tells me things that are wrong... Thanks sooooo much! (:

Answer 19

So if that's the case let's go back to your original problem

Answer 20

What is \(10(1.0605)^0\)

Answer 21

Alright. so then it would be 10,00

Answer 22

Correct? (:

Answer 23

Exactly.

Answer 24

Nice work.

Answer 25

Haha! Nope the credit goes to you (: Thanks a bunch!