Question

Since 2013 median home prices in Midvale, UT have been growing exponentially according to the model Pₜ=P₀ (1+r)ᵗ with a growth rate of roughly 4.7% per year. If you had purchased a house in Midvale, UT for $147000 in 2014 in what year would the home be worth $239000?

Answer 1

To determine when a house bought for $147,000 in 2014 would be worth $239,000 with a 4.7% annual growth, apply the exponential growth formula to find that approximately 9.53 years are needed. Adding this to 2014, the home's worth will reach $239,000 around the year 2023 or 2024.

Step-by-step explanation:

To calculate in what year a home in Midvale, UT purchased for $147,000 in 2014 would be worth $239,000, given a growth rate of 4.7% per year, use the exponential growth model Pt = P0 (1 + r)t. We are given P0 = $147,000, Pt = $239,000 and r = 0.047 (4.7% as a decimal). Solving for t:

• $239,000 = $147,000 (1 + 0.047)t
• $239,000 / $147,000 = (1.047)t
• 1.62585 = 1.047t

Apply the logarithm to both sides to solve for t:

• log(1.62585) = t * log(1.047)
• t = log(1.62585) / log(1.047)

Calculate t to find the number of years:

• t ≈ 9.53 years

Since the purchase year is 2014, add t to find the year when the home value reaches $239,000:

• 2014 + 9.53 ≈ 2023 or 2024

The home would be worth $239,000 in approximately the year 2023 or 2024.