The precise equation that represents the situation is as follows:
- $19, x ≤ 300
- x > 300,
- f(x) = 19 + 0.39(x - 300)
<h3>How to represent an equation?</h3>
His cell phone plan provides 300 free minutes each month for a flat rate of $19.
let
x = number of minutes used
Therefore,
$19, x ≤ 300
For any minutes over 300, Andrew is charged 0.39 per minute.
Therefore,
if x > 300
f(x) = 19 + 0.39(x - 300)
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The expression y = 4.998 ·
is the exponential function that passes through the points (- 1, 5 / 3) and (3, 135).
<h3>How to derive an exponential function that passes through two given points</h3>
Herein we find the location of two points set on Cartesian plane that belongs to an exponential function of the form:

Where:
- A - y-Intercept of the exponential function.
- B - Growth factor
- x - Independent variable.
- y - Dependent variable.
Which is equivalent to the following logarithmic expression:
㏑ y = ㏑ A + B · x
If we know that (x₁, y₁) = (- 1, 5 / 3) and (x₂, y₂) = (3, 135), then the following system of equations is generated:
㏑ (5 / 3) = ㏑ A - B
㏑ 135 = ln A + 3 · B
Then, we solve the system by numerical methods:
㏑ A = 1.609 (A = 4.998), B = 1.098
And the exponential function is equal to y = 4.998 ·
.
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John will receive $9.80 back
15 is 25% of 60 because 25% is .25 in decimal form which 1/4 in fraction form and 1/4(60)=15