Question

Which functions in the table below give values that could come from exponential functions?

Answer 1

x increases by 1 each time.
See how f(x) increases. Take the difference in f(x) values:
3, 5, 7, 9, ....
Take the difference again: 2, 2, 2, ...
So the second differences of f(x) are constant.
This implies f(x) is quadratic and not exponential

Answer 2

See how g(x) increases.
It is doubling every time. 0.125 x 2 = 0.25; 0.25 x 2 = 0.5; 0.5 x 2 = 1, ...
This is a geometric sequence. Therefore it is an exponential function.

Answer 3

Can you do the last two?

Answer 4

ohhh so is h(x) is one right?

Answer 5

h(x) increases by the SAME amount every time. It increases by 0.25.
So it is an arithmetic sequence which is linear or a straight line.
So h(x) is NOT exponential.

Try the last one.

Answer 6

but doesn't k(x) go down?

Answer 7

Yes, it does. Exponential GROWTH function will go up but exponential DECAY function will go down. So just because it goes down you can't say it is not exponential.

Answer 8

Observe the pattern and see what is happening to the k(x) values each time x increases by 1.

Answer 9

How to get from 64 to 16?
From 16 to 4?

Is there a pattern?

Answer 10

Yea...but idk what

Answer 11

How to go from 64 to 16? You divide by 4.
How to go from 16 to 4? You divide by 4.

So the pattern is you divide by 4 each time.
This is a geometric sequence with a common ratio of 1/4.
Therefore, it is an exponential function.

(BTW, there is a mistake in the table they gave you.
When x = 0, k(x) must be 1 and not 0.)

Answer 12

ohhhhhh wow thank so much for explaining it out like that to me. Do you think you can help me with another question?

Answer 13

Close this one post a new one and tag me. In the meantime there are others who have tagged me and I will come to you after that.

Answer 14

ok thankyou :)