The statement that is true about the given table is "The situation can be modelled by an exponential decay function with a percent change of -10%".
What is exponential growth or decay function?
Consider the function:
y= a(1 ± r)ˣ
where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
- If there is a plus sign, then there is exponential growth happening by r fraction or 100r %
- If there is a negative sign, then there is exponential decay happening by r fraction or 100r %
Given that An event management company purchases a new van. The value of the van, x years after the purchase, is shown in the table.
Now, if the rate of decay and the initial price of the van can be found by substituting the value of x and y in the equation as shown below.
For the first column from the table, when the value of x and y is 0 and 20,000, respectively.
y= a(1 + r)ˣ
20,000 = a(1 + r)⁰
20,000 = a (1)
a = 20,000
For the second column from the table, when the value of x and y is 1 and 18,000, respectively. Also, the value of a=20,000.
y= a(1 + r)ˣ
18,000 = 20,000(1 + r)¹
18,000/ 20,000 = 1 + r
0.9 = 1 + r
0.9 - 1 = r
-0.1 = r
r = -0.1 = -10%
Hence, the statement that is true about the given table is "The situation can be modelled by an exponential decay function with a percent change of -10%".
Learn more about Exponential Growth and Decay here:
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