Question

You have inherited land that was worth 30,000 in 2000. The value of the land V increases according to the model V=30,000(1.04)^t where t is the number of years since 2000. The land will be worth 90,000 in what year?

Answer 1

AplWe are given that the value of land increases according to the following function:

`V=30,000\left(1.04\right)^t`

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:

`30000\left(1.04\right)^t=90000`

Now, we solve for "t". To do that we will divide both sides by 30000:

`(1.04)^t)=(90000)/(30000)`

Solving the operations:

`(1.04)^t=3`

Now, we take the natural logarithm to both sides:

`ln(1.04)^t=ln3`

Now, we use the following property of logarithms:

`lnx^y=ylnx`

Applying the property we get:

`tln(1.04)^=ln3`

Now, we divide both sides by ln(1.04):

`t=(ln3)/(ln1.04)`

Solving the operations:

`t=28`

This means that the land will be worth $90000 28 years since 2000, therefore, the year is 2028