Explain, in general terms, how the portions of loan payments going to principal and interest change over the life of the loan.

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azainababbas

06.06.2020

Mathematics

The piecewise function is:

$C(x) = C(x) = \left \{ {{4, 0< x \leq 1} \atop {4 + 8x, 1 < x \leq 2}}\right.$

Step-by-step explanation:

A piecewise function is a function that is defined in multiple intervals.

In the first interval:

$0 < x \leq 1$

The problem states that a taxi company charges $4.00 for the first mile (or part of a mile).

x is the number of miles. So

If $x \leq 1, C(x) = $4.00$ .

Second interval:

$1 < x \ leq 2$

Here, the cost is defined by a linear function in the following format:

$C(x) = C_{0} + rx$

In which $C_{0}$ is the initial price and r is the price paid per mile.

The problem states that each succeeding tenth of a mile costs 80 cents. So

we have the following rule of three.

1 mile - r dollars

0.1miles - 0.8 dollars

0.1r = 0.8

$r = \frac{0.8}{0.1}$

r = 8

So, we have

$C(x) = 4 + 8x, 1 < x \leq 2$

Piecewise function:

The piecewise function is:

$C(x) = C(x) = \left \{ {{4, 0< x \leq 1} \atop {4 + 8x, 1 < x \leq 2}}\right.$

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