Question

The price f(x), in dollars, of product A after x years is represented by the function below:

f(x) = 72(1.25)x

Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)

Part B: The table below shows the price f(t), in dollars, of product B after t years:


t (number of years) 1 2 3 4
f(t) (price in dollars) 65 84.5 109.85 142.81
Which product recorded a greater percentage change in price over the previous year?

Answer 1

Please do yourself and others a favor by expressing exponentiation properly.
f(x) = 72(1.25)x is incorrect; you mean\[f(x) = 72(1.25)^x.\]

Answer 2

Evaluate 1.25^x at 0, 1, 2, 3. Is this factor increasing or decreasing or remaining the same?

Answer 3

I copied and pasted the question so idk what you are talking about.. ._.

Answer 4

and its decreasing

Answer 5

@mathmale

Answer 6

Copying and pasting does not always put the exponent (x) in the correct place.

75(1.25)^x denotes exponentiation: It's 1.25, raised to the power x, and then the result is multiplied by 75.

As before, I ask you to evaluate 1.25^x for x=0, 1, 2, 3. Is this function increasing or decreasing as x increases?

Answer 7

idk.. @mathmale

Answer 8

(any number other than zero)^0=1.

Therefore, 1.25^0 = ?

1.25^1 = ?

Answer 9

0

Answer 10

@mathmale

Answer 11

1.25^0 does not equal 0. That 0 is an exponent.

Note that 2^0 = 1.

3^0 =1.

What is 1.25^0?

Answer 12

1? @mathmale

Answer 13

Yes, that's right. What is 1.25^1? 1.25^2? iF YOU'RE

Answer 14

If you're not sure, review exponentiation, please.

Answer 15

Ok so whats next? @mathmale

Answer 16

Have you found 1.25^1, 1.25^2 and 1.25^3 yet?

Answer 17

As x increases, does 1.25^x increase, decrease or stay the same?

Answer 18

If you can answer this correctly, you will have essentially answered part A of your question.

Answer 19

B: Sorry this discussion has dragged on and on. But if you go back and review it, you'll see that there were several occasions on which you didn't follow through. For example,
I asked you to evaluate 1.25^1, 1.25^2 and 1.25^3.

Hope we can finish up this problem later on.