Brad bought a piece of industrial real estate for $192,345. The value of the real estate appreciated a constant rate per year. The table shows the value of the real estate after the first and second years:

Year:
1
2

Value (in dollars):
$200,038.80
$208,040.35

Which function best represents the value of the real estate after t years?
A. f(t) = 200,038.80(1.04)^t

B. f(t) = 200,038.80(0.04)^t

C. f(t) = 192,345(0.04)^t

D. f(t) = 192,345(1.04)^t

Also that is the original price and when you look at exponential functions, the starting point or original price is always first the then rate of increase. The table just shows how it increased in year 1 and 2.

Hope this helps. :)

Answer Link

ap8997154 ap8997154 · Answer 2 · 2022-07-14T09:42:19+02:00

A function assigns the values. The function that best represents the value of the real estate after t years is f(t) = 192,345(1.04)^t. Thus, the correct option is D.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The initial cost of industrial real estate is $192,345, while the cost after one year is $200,038.80. Therefore, the rate of appreciation is,

[tex]\$200,038.80 = \$192,345(1+R)^t\\\\\$200,038.80 = \$192,345(1+R)^1\\\\\dfrac{\$200,038.80}{\$192,345}=(1+R)^t\\\\1.04 = 1 + R\\\\R = 0.04[/tex]

Hence, the function that best represents the value of the real estate after t years is f(t) = 192,345(1.04)^t. Thus, the correct option is D.

Learn more about Function:

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