Choose all that represent an exponential function-
a. x | -3 | -2 | -1 | 0 | 1 | 2 | 3
y | 14 | 10 | 6 | 2 | -2 | -6 | -10
b. x | -3 | -2 | -1 | 0 | 1 | 2 | 3
y | 1/2 | 1 | 2 | 4 | 8 | 16 | 32
c. x | -3 | -2 | -1 | 0 | 1 | 2 | 3
y | -14 | -9 | -4 | 1 | 6 | 11 | 16
d. x | -3 | -2 | -1 | 0 | 1 | 2 | 3
y | 4 | 8 | 16 | 32 | 64 | 128 | 256
I am sorry they are not lined up! I tried my best and I believe the answers are C and D. Can someone check for me?
Nope. Exponentials keep multiplying by the same amount.
A and C just add the same amount each time.
B multiplies by 2, so it is 4*2^x
D multiplies by 1/2 each time, so it is 32 * 1/2^x = 32*2^-x
hint: in the last function, .....
4 = 2^2
8 = 2^3
16 = 2^4
what pattern do you see
I notice something similar in b)
Yes, you are correct! The exponential functions are represented by the data sets in options C and D:
c. x | -3 | -2 | -1 | 0 | 1 | 2 | 3
y | -14 | -9 | -4 | 1 | 6 | 11 | 16
d. x | -3 | -2 | -1 | 0 | 1 | 2 | 3
y | 4 | 8 | 16 | 32 | 64 | 128 | 256
These data sets show exponential growth, where the value of y increases exponentially as x increases.
To determine if a function is exponential, we need to check if the ratio between consecutive y-values remains constant as the x-values increase or decrease by a constant amount.
For option a:
The ratio between consecutive y-values is -4/4 = -1, which is not constant. Therefore, option a is not an exponential function.
For option b:
The ratio between consecutive y-values is 1/2 = 0.5, which is constant. Therefore, option b is an exponential function.
For option c:
The ratio between consecutive y-values is 6/5 = 1.2, which is not constant. Therefore, option c is not an exponential function.
For option d:
The ratio between consecutive y-values is 8/4 = 2, which is constant. Therefore, option d is an exponential function.
Therefore, the correct choices are options b and d.