identify y= 3 (1.2)^x as an example of growth or decay. what is the y- intercept.
Is it a growth or deacy?
for y = a*b^x
growth if b > 1
decay if b < 1
In your case, since 1.2^0 = 1, the y-intercept is at (0,3)
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Growth or decay
Well, let's analyze the equation y = 3(1.2)^x to determine if it represents growth or decay.
Since the base of the exponent is 1.2, which is greater than 1, we can conclude that it represents growth. If the base were less than 1, then we would be looking at decay.
As for the y-intercept, it's the value of y when x is equal to 0. So, substituting x = 0 into the equation, we get:
y = 3(1.2)^0
y = 3(1)
y = 3
Therefore, the y-intercept is 3.
To identify whether the equation y = 3(1.2)^x represents growth or decay, you need to examine the base of the exponential term.
In this equation, the base is 1.2.
If the base is greater than 1, then the equation represents exponential growth.
If the base is between 0 and 1 (exclusive), then the equation represents exponential decay.
Since the base in y = 3(1.2)^x is 1.2, which is greater than 1, the equation represents exponential growth.
Now, to find the y-intercept, you can substitute x = 0 into the equation and solve for y.
When x = 0:
y = 3(1.2)^0
y = 3(1)
y = 3
Therefore, the y-intercept is 3.