Find the equation of the exponential function represented by the table below
1 answer:
Answer:
Step-by-step explanation:
Exponential functions are represented in the form , where a is the initial value and b is the multiplier.
Here, we see that when x = 0, y = 4. This means that 4 is our initial value, or a. You can look at the a variable almost being like the y-intercept of a graph.
Next, we must solve for b. We can do 16 ÷ 4 to find the slope, or multiplier of this function, because 16 is 1 input x-value up from 0. 16 ÷ 4 = 4.
So, we now have all the needed variables, so we plug them into the formula
You might be interested in
Answer:
Growth when: b>1.
Decay when: 0<b<1.
Step-by-step explanation:
Any function in the form , where a > 0, b > 0 and b not equal to
is called an exponential function with base b.
If 0 < b < 1 this is an example of an exponential decay.
The general shape of an exponential with b > 1 is an example of exponential growth.
Hence,
An exponential function is expressed in the form , The relation represents a growth when b >1 and a decay when 0<b<1.