Answer :
Using an exponential function, we have that:
a) The equation is: [tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex].
b) The house will have a value of $1 million during the year of 2037.
c) The expected value on April 1, 2020, is of $621,520.
What is an exponential function?
An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
- A(0) is the initial value.
- r is the growth rate, as a decimal.
In this problem, the parameters are given as follows:
A(0) = 600000, r = 0.058 each 2 years.
Hence the exponential function is:
[tex]A(t) = 600000(1 + 0.058)^{\frac{t}{2}}[/tex]
[tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex]
Item b:
It is the year 2019 + t, for which A(t) = 1000000, hence:
[tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex]
[tex]1000000 = 600000(1.058)^{0.5t}[/tex]
[tex](1.058)^{0.5t} = 1.6667[/tex]
[tex]\log{(1.058)^{0.5t}} = \log{1.6667}[/tex]
[tex]0.5t\log{1.058} = \log{1.6667}[/tex]
[tex]t = \frac{\log{1.6667}}{0.5\log{1.058}}[/tex]
[tex]t = 18.12[/tex]
The house will have a value of $1 million during the year of 2037.
Item c:
April 1, 2020 is one year and 3 months = 1.25 years after January 1, 2019, hence the value of the home will be given by:
[tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex]
[tex]A(1.25) = 600000(1.058)^{\frac{1.25}{2}}[/tex]
A(1.25) = $621,520.
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1