The exponential growth is given by the growth rate of subsequent period
raised to power of time.
The Correct Responses;
- The exponential growth function is; f(28) = (1 +0.06)²⁸
- The value of the basketball card in 2015 is approximately $38.34
Methods used to obtain the above response;
The given parameter are;
The amount Aaron buys the basketball card in 1987, a = $7.50
The rate at which the value increases each year, r = 6%
Required:
To write the exponential growth function.
A general form of the exponential growth function is; [tex]f(t) = \mathbf{ a \cdot (1 + r)^t}[/tex]
Where;
a = The starting amount = $7.50
r = The growth rate = 6% = 0.06
t = The time duration of the growth = 2015 - 1987 = 28
The time duration, t = 28 years
Solution:
The exponential growth function to find the basketball card's value in 2015 is therefore;
- Value in 2015 = [tex]\underline{f(28) = (1 + 0.06)^{28}}[/tex]
Which gives;
f(28) = 7.5 × (1 + 0.06)²⁸ ≈ 38.34
- The value of the basketball card in 2015 is approximately $38.34
Learn more about the exponential growth function here:
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