Question 905323: Determine whether the function is an example of exponential decay or growth ? Explain how you know and then find the y-intercept.
y= 3(0.25)^x
Found 2 solutions by Theo, AlgebraLady88:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe this will be delay.
lere's why.
year 0 you get 3 * .25^0 = 3 * 1 = 3
year 2 you get 3 * .25^1 = 3 * .25 = .75
year 3 you get 3 * .25^2 = 3 * .0625 = .1875
the numbers are decreasing year after year so you are talking about decay.
b^x increases as x increases if b is greater than 1.
b^x stays the same as x increases if b is equal to 1.
b^x decreases as x increases if b is greater than 0 and less than 1.
x is assumed to be greater than or equal to 0.
Answer by AlgebraLady88(44)  (Show Source):
You can put this solution on YOUR website! Remember that there are two ways to tell whether a graph is an example of exponential decay or exponential growth.
A graph that is decreasing or showing exponential decay :
y= ab^x
where a > 0 and b is between 0 and 1 .
For example, in y= 200 ( 0.5) ^ x , each time x is increased by 1, y is decreased by 1/2 of its previous value.
A graph that is showing increasing growth :
y= ab^x
where a >0 and b is greater than 1 , the graph will be increasing.
For this example, we have 3(0.25)^x, and we can see that b is between 0 and 1, so that's why this is a graph of exponential decay, where each time x is increased by 1 , we see that y is decreased by 1/4 of its previous value.
y= 3(0.25)^1 = 0.75
y= 3(0.25)^2 = 0.1875 (this is 1/4 of 0.75)
y= 3(0.25)^3 = 0.046875 (this is 1/4 of 0.1875)
y= 3(0.25)^4 = 0.0117188(this is 1/4 of 0.046875)
To find the y intercept, we would designate x=0. Why? Any y intercept, whether of a linear or exponential graph ,would always have 0 as the value of x.
So, y= 3(0.25)^0
y= 3 (1)
y= 3.
Note:anything to the power of zero is always 1.
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