pre calc question

Question

A house was valued at $110,000 in the year 1987. The value appreciated to $170,000 by the year 2007.

A) What was the annual growth rate between 1987 and 2007?

r =  Round the growth rate to 4 decimal places.

B) What is the correct answer to part A written in percentage form? 

r =  %.

C) Assume that the house value continues to grow by the same percentage. What will the value equal in the year 2011 ?

value = $   Round to the nearest thousand dollars

Answer 1

A) To find the annual growth rate between 1987 and 2007, we can use the following formula:

r = (Vf/Vi)^(1/n) - 1

where Vf is the final value (in 2007), Vi is the initial value (in 1987), n is the number of years between the initial and final values, and r is the annual growth rate.

In this case, Vf = $170,000, Vi = $110,000, and n = 2007 - 1987 = 20. Substituting these values into the formula, we get:

r = ($170,000/$110,000)^(1/20) - 1 r ≈ 0.0341

So the annual growth rate between 1987 and 2007 was approximately 0.0341.

B) To express the annual growth rate as a percentage, we can multiply by 100:

r = 0.0341 * 100 r ≈ 3.41%

So the annual growth rate between 1987 and 2007 was approximately 3.41%.

C) If we assume that the house value continues to grow by the same percentage, we can use the following formula to find its value in the year 2011:

Vf = Vi * (1 + r)^n

where Vi is the initial value (in 1987), r is the annual growth rate, n is the number of years from the initial value to the desired year (2011), and Vf is the final value.

In this case, Vi = $110,000, r = 0.0341, n = 2011 - 1987 = 24. Substituting these values into the formula, we get:

Vf = $110,000 * (1 + 0.0341)^24 Vf ≈ $261,154

So the value of the house in the year 2011 would be approximately $261,000 (rounded to the nearest thousand dollars).