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The piece-wise linear functions can be written as follows:
.
.
.
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
For x equal or less than -2, the line passes through (-3,-3) and (-2,-2), hence the rule is:
.
For x greater than -2 up to 1, the y-intercept is of -7, and the line also passes through (1,-8), hence the rule is:
.
For x greater than 1, the function goes through (2,-5) and (3,-3), hence the slope is:
m = (-3 - (-5))(3 - 2) = 2.
The rule is:
y = 2x + b.
When x = 2, y = -5, hence:
-5 = 2(2) + b
b = -9.
Hence:
.
More can be learned about linear functions at brainly.com/question/24808124
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Solution:
Given:
when a = 4, substitute for a in the expression;
Therefore, if (a = 4), then
Hence, the answer is 16.
Answer:
$39,851.25
Step-by-step explanation:
If the sales increase at a rate of 9% per year, this means it will be 109% of the previous year's value since 100% + 9% = 109%
109% in decimal form = 109/100 = 1.09
Therefore, the exponential function is:
, where
is the number of years
So when ,
After 8 years, annual sales = $39,851.25