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Mathematics

1 answer:

Sladkaya [172]2 years ago

6 0

Using linear function concepts, it is found that:

a) The initial value is of 3 and the rate of change is of 20.

b) The rate of change means that for each hour, the cost increases by 3 Dhs, while the initial value means that a flat fee of 20 Dhs is paid.

<h3>What is a linear function?</h3>

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 also can be considered as the initial value.

In this problem, the function that gives the charge C for renting a bicycle for h hours is:

$C(h) = 3h + 20$

Item a:

Comparing to the standard function, we have that:

The initial value is of 3 and the rate of change is of 20.

Item b:

The rate of change means that for each hour, the cost increases by 3 Dhs, while the initial value means that a flat fee of 20 Dhs is paid.

You can learn more about linear function concepts at brainly.com/question/24808124

You might be interested in

Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5

zaharov [31]

Answer:

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}$ or $\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

$\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}$

Therefore, the solution is 31.

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as $\displaystyle \large{a_{n-1} \cdot r = a_n}$ meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as: