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Question 1188487: Please help me solve this problems:
Suppose the sales of Nin Jao study table satisfy the function rule 𝑁(𝑥) = 100(3𝑥 + 20), where 𝑁(𝑥)
represents the number study tables sold in 𝑥 years, with 𝑥 = 0 corresponding to the production year
2012. Find the sales in each of the following years:
a. 2012
b. 2013
c. 2018
d. 2021
What is the annual rate of change of the sale? Make a table of values for the problem and graph it.
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52798)   (Show Source):
You can put this solution on YOUR website! .
D U P L I C A T E
I just answered it under this link
https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1188437.html
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! 2012 is the base year.
when the year is:
2012, x = 2012 - 2012 = 0, and n(x) = 100 * (3 * 0 + 20) = 100 * 20 = 2000
2013, x = 2012 - 2012 = 1, and n(x) = 100 * (3 * 1 + 20) = 100 * 23 = 2300
2018, x = 2018 - 2012 = 6, and n(x) = 100 * (3 * 6 + 20) = 100 * 38 = 3800
2021, x = 2021 - 2012 = 9, and n(x) = 100 * (3 * 9 + 20) = 100 * 47 = 4700
the equation of n(x) = 100 * (3 * x + 20) can be graphed.
i replaced n(x) with y and graphed it, as shown below.
the graphing software i used can be found at https://www.desmos.com/calculator
this is a linear equations.
it can be transformed into the slope intercept form of a linear equation as follows:
replace n(x) with y.
start with y = 100 * (3 * x + 20)
simplify to get:
y = 100 * 3 * x + 100 * 20
simplify further to get:
y = 300 * x + 2000
the equation is now in slope intercept form.
the slope is 300 and the y-intercept is 2000.
this means that y = 2000 when x = 0 (y-intercept) and, for every increase of 1 in the value of x, the corresponding value of y increased by 100.
x = 0, y = 2000
x = 1, y = 2300
x = 2, y = 2600
etc.
the annual rate of change is the slope which is equal to 300.
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