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The number of baskets a company produces each day is shown in the table.a. Write an equation to find the total number of baskets crafted in any number of days. Describe the relationship in words.b. Use the equation to determine how many baskets the company makes in one non-leap year.

The Number Of Baskets A Company Produces Each Day Is Shown In The Tablea Write An Equation To Find The Total Number Of Baskets Crafted In Any Number Of Days Des class=

Sagot :

a)

The first day the company made 45 basktes, afterwards the company makes the same amount of baskets each day. You can express the number of baskets made after any number of days by using an arithmetic sequence.

The first number of the sequence will be the baskets made for day 1

a=45

To determine the common difference of the sequence, that is, the number of baskets they make each passing day, you have to calculate the difference between one value of the sequence and the prevoius one.

In this case, on day 3 they made 135 basktets and the previous value, day 2, is equal to 90 baskets, the common difference is then:

[tex]d=135-90=45[/tex]

This means that each passing day the make 45 new baskets.

To calculate the number of baskets made in any "nth" day you can use the following formula:

[tex]x_n=a+d(n-1)[/tex]

Where

a is the first value of the sequence

d is the common difference

n represents the place of the value in the sequence

x is the value of the sequence

So for this exercise the equation will be:

[tex]x_n=45+45(n-1)[/tex]

b)

A non leap year has 365 days, if you have to calculate the number of baskets made after a non-leap year, this means that you have to calculate the sequence for n=365

[tex]\begin{gathered} x_{365}=45+45(365-1) \\ x_{365}=45+45\cdot364 \\ x_{365}=45+13680 \\ x_{365}=16425 \end{gathered}[/tex]

The number of baskets made after a non-leap year is 16425

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