Question

Exponential & Logarithmic Functions

Please Help ASAP! The question is in the picture.

Sam purchases a house for $150,000 near Thurmond Lake. The value of houses in the area where the house was purchased is averaging an increase of 7% per year.

What would be the growth factor (multiplier)?

If the trend continues how much would the house be worth 12 years after Sam purchased the house?

Answer 1

The growth factor for an annual increase of 7% is 1.07. To calculate the future worth of a house after 12 years, we apply the exponential growth formula, resulting in a future value of $337,800.

Step-by-step explanation:

The student is asking about the growth factor and future value of a house with an annual increase in value of 7%. To find the growth factor, we simply add the percentage increase to 1. Hence, the growth factor in this case is 1 + 0.07 = 1.07. To find the house's worth 12 years after purchase, we use the formula for exponential growth:

Future Value = Present Value * (Growth Factor)^number of periods. Substituting the given values, we get:

• Future Value = $150,000 * (1.07)^12
• Future Value = $150,000 * 2.252
• Future Value = $337,800

Assuming the trend continues, the house would be worth $337,800, 12 years after Sam purchased it.

Answer 2

What would be the growth factor (multiplier)?

Continuously compounded:

e or 2.718.

Simple interest:

1.84

If the trend continues how much would the house be worth 12 years after Sam

purchased the house?

Continuously compounded:

$347,455.05

Simple interest:

$276,000.00

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Step-by-step explanation: