SOLUTION: 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

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.

RELATED QUESTIONS
Determine whether the function represents exponential growth or exponential decay then... (answered by tommyt3rd)
The population of the United States has been changing at an exponential rate since the... (answered by stanbon)
Without graphing, determine whether the function y = 7(0.28)^x represents exponential... (answered by jim_thompson5910)
Please help me write an exponential function whose graph passes through the points (0,-5) (answered by scott8148)
I would like to know how to figure out if a function is NEITHER exponential growth or... (answered by stanbon)
Determine whether the equation represents exponential growth, exponential decay, or... (answered by MathLover1)
Without graphing, determine whether the function y = 7{2/3}^x represents exponential... (answered by jsmallt9)
Is this function for exponential growth or decay? Find the constant percentage rate of... (answered by oscargut)
Determine whether the equation represents exponential growth, exponential decay, or... (answered by greenestamps,Theo)