P/2 is less than or equal to negative 3
2 answers:
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We have
so this is indeed a difference of squares. Factorizing would give
making the answer D.
We can further factor the first term here and write
but that's clearly out of the scope of this question.
Answer:
A) 3%
B) Product A
Step-by-step explanation:
<u>Exponential Function</u>
General form of an exponential function:
where:
- a is the initial value (y-intercept)
- b is the base (growth/decay factor) in decimal form
- x is the independent variable
- y is the dependent variable
If b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
<u>Part A</u>
<u>Product A</u>
Assuming the function for Product A is <u>exponential</u>:
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:
⇒ 1.03 - 1 = 0.03 = 3%
Therefore, <u>product A is increasing by 3% each year.</u>
<u>Part B</u>
To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:
Check using different two consecutive values of f(t):
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)
To check this, substitute the values of t for 1 through 4 into the found function:
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>