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AysviL [449]
2 years ago
15

What is the equation of the function that is graphed as line b?

Mathematics
1 answer:
Juli2301 [7.4K]2 years ago
5 0

Following the slope of the line at x= 0 the line is at y =1 , at x=, it is at Y = 1.5, so the slope is 1/2

The y intercept is where the line crosses the y a is at x =0 which is 1

The equation would be y = 1/2x+ 1

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The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price
likoan [24]

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A)  3%

B)  Product A

Step-by-step explanation:

<u>Exponential Function</u>

General form of an exponential function: y=ab^x

where:

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  • x is the independent variable
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If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

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<u>Product A</u>

Assuming the function for Product A is <u>exponential</u>:

f(x) = 0.69(1.03)^x

The base (b) is 1.03.  As b > 1 then it is an <u>increasing function</u>.

To calculate the percentage increase/decrease, subtract 1 from the base:

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Therefore, <u>product A is increasing by 3% each year.</u>

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\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100

To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:

\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%

Check using different two consecutive values of f(t):

\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%

Therefore, as 3% > 1%, <u>Product A recorded a greater percentage change</u> in price over the previous year.

Although the question has not asked, we can use the given information to easily create an exponential function for Product B.

Given:

  • a = 10,100
  • b = 1.01
  • n = t - 1 (as the initial value is for t = 1 not t = 0)

\implies f(t) = 10100(1.01)^{t-1}

To check this, substitute the values of t for 1 through 4 into the found function:

\implies f(1) = 10100(1.01)^{1-1}=10100

\implies f(2) = 10100(1.01)^{2-1}=10201

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\implies f(4) = 10100(1.01)^{4-1}=10406.04

As these values match the values in the given table, this confirms that the found function for Product B is correct and that <u>Product B increases by 1% per year.</u>

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2 years ago
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Step-by-step explanation:

my noggin

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