Answer:
$27402.
Step-by-step explanation:
We have been given that Berto invested in a precious mineral. The value of the mineral tends to increase by about 11% per year. He invests $40,000 in 2015.
Let us write a function using our given information for the value of minerals.
We are told that the value of minerals increase by 11% every year, so our function will be an exponential function.
Since an exponential function is in form: [tex]y=a*b^x[/tex]; for growth b=(1+r), where r is rate of growth in decimal form.
a= Initial value.
Let us convert our given rate in decimal form.
[tex]11 percent= \frac{11}{100}=0.11[/tex]
Let G(t) be the growth of minerals t years after 2015.
Upon substituting our given values we will get our function as: [tex]G(t)=40,000*(1+0.11)^t[/tex]
[tex]G(t)=40,000*(1.11)^t[/tex]
To find the value of Berto's investment in year 2020 by substituting t=5 in our function as 2020-2015=5.
[tex]G(2020)=40,000*(1.11)^5[/tex]
[tex]G(2020)=40,000*1.6850581551[/tex]
[tex]G(2020)=67402.326204\approx 67402[/tex]
Therefore, the value of his investment in 2020 will be $67402.
Let us find the difference of values of minerals between 2020 and 2015.
67402-40000=27402
Therefore, Berto's investment will be worth $27402 in 2020.
