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Sagot :
AplWe are given that the value of land increases according to the following function:
[tex]V=30,000\left(1.04\right)^t[/tex]We are asked to determine the value of "t" for which the value of the function is 90000.
to so that we will set the function equal to 90000:
[tex]30000\left(1.04\right)^t=90000[/tex]Now, we solve for "t". To do that we will divide both sides by 30000:
[tex](1.04)^t)=\frac{90000}{30000}[/tex]Solving the operations:
[tex](1.04)^t=3[/tex]Now, we take the natural logarithm to both sides:
[tex]ln(1.04)^t=ln3[/tex]Now, we use the following property of logarithms:
[tex]lnx^y=ylnx[/tex]Applying the property we get:
[tex]tln(1.04)^=ln3[/tex]Now, we divide both sides by ln(1.04):
[tex]t=\frac{ln3}{ln1.04}[/tex]Solving the operations:
[tex]t=28[/tex]This means that the land will be worth $90000 28 years since 2000, therefore, the year is 2028
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