Question

Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the function.

x
0
1
2
3
4
f (x)
12.5
13.75
15.125
16.638
18.301

Answer 1

If a function is linear, the y values will increase/decrease by a number that is added to the previous factor. If a function is exponential, the y values will increase/decrease by a number that the previous factor is multiplied by.

Linear: x, x+2, x+4, x+6
Exponential: x, 2x, 4x, 8x

Answer 2

What do i do next?

Answer 3

If you know what type of function you have, you write a general formula.
What type of function is this?

Answer 4

it's linear

Answer 5

noo exponential

Answer 6

good, its exponential because you multiply each y value by a factor of 1.1 to get to the next y value. Now you write the general formula for the sequence.

Answer 7

The general formula for a geometric (exponential) sequence is the number that you are multiplying one y value by to get to the next one to the power of the corresponding x value plus some number.

So what you have so far is y=1.1^(x+?)

You can solve for your unknown by plugging in an (x,y)

Its easiest to use 0 as your x, so we'll plug in the coordinate (0,12.5)

12.5=1.1^(0+?)

Now to find the value of the unknown, you write a log

log(12.5) = (0+?)log(1.1)

divide both sides by log 1.1

0+? = approximately 26.5

You use this number for every equation, and the x and y values change, so if you wanted to find the y value for x=5, you would do:

y=1.1^(5+26.5)

y=1.1^(31.5)

y= 20.131