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A patch of farmland is currently worth $78,125. The expected increase in its market value can be modeled by the function below, where t is the time in years. How many years will it take for the farmland's market value to reach $125,000?

Sagot :

The number of the years to take for the farmland's market value to reach $125,000 will be 19 years.

The missing function will be given below.

[tex]\rm p(t) = 78,125\ e^{0.025t}[/tex]

What is an exponent?

Let a is the base and x is the power of the exponent function and b is the y-intercept. The exponent is given as

y = aˣ

A patch of farmland is currently worth $78,125. The expected increase in its market value can be modeled by the function below.

[tex]\rm p(t) = 78,125\ e^{0.025t}[/tex]

Then the number of the years to take for the farmland's market value to reach $125,000 will be

[tex]\rm 78,125 \ e^{0.025t} = 125,000\\\\e^{0.025t} = 1.6[/tex]

Then take log on both sides, then we have

0.025t lne = ln 1.6

     0.025t = 0.47

               t = 18.8

               t = 19 years

More about the exponent link is given below.

https://brainly.com/question/5497425

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