In 19977, a math professor bought her condominium for $60,000. The value of the condo has risen steadily so that in 2007 real estate agents tell her the condo is now worth $750,000. Find a formula to represent these facts about the value of the condo V (t), as a function of time,t, where t is in years after 1977.
The question says that the value has risen steadily, so I'm going to assume each year, the amount increased in the same.
Total Value - Initial Value = Amount increased
750,000 - 60,000 = 690,000
Total years:
2017-1977 = 40 years
Amount increased each year:
690,000/40 = 17250
V(t) = initial amount + amount increased each year x t
Answer:
V(t) = 60000+17250*t
750,000 - 60,000 = 690,000
2017-1977 = 30 years
690,000/30 = 23,000
V(t) = initial amount + amount increased each year •t
Answer: V (t)=60,000+23,000t
To find a formula that represents the value of the condo (V) as a function of time (t), we can use the given information.
In 1977, the value of the condo was $60,000 (when t = 0).
In 2007, the value of the condo was $750,000 (when t = 30).
To find a linear equation that represents the increase in value over time, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
The slope (m) can be calculated as the change in the value (ΔV) divided by the change in time (Δt):
m = (ΔV) / (Δt) = (750,000 - 60,000) / (30 - 0) = 690,000 / 30 = 23,000
Since the y-intercept (b) is the value of the condo in 1977 ($60,000), we can substitute these values into the equation:
V(t) = 23,000t + 60,000
Therefore, the formula representing the value of the condo as a function of time (t) would be:
V(t) = 23,000t + 60,000
To find a formula that represents the value of the condo, we can identify the initial value in 1977 and the constant rate of increase from 1977 to 2007.
Step 1: Identify the initial value in 1977
We are given that in 1977, the math professor bought the condo for $60,000. Therefore, the initial value in 1977 is $60,000.
Step 2: Determine the rate of increase
From 1977 to 2007, the value of the condo rose steadily. To find the rate of increase, we can subtract the initial value from the final value and divide by the number of years.
Final value - Initial value = Rate of increase × Number of years
$750,000 - $60,000 = Rate of increase × 30 (since 2007 - 1977 = 30 years)
$690,000 = Rate of increase × 30
Divide both sides of the equation by 30:
Rate of increase = $690,000 / 30
Rate of increase ≈ $23,000 per year
Step 3: Write the formula
Now we have the initial value of $60,000 and the rate of increase of approximately $23,000 per year.
V(t) = Initial value + (Rate of increase × t)
V(t) = $60,000 + ($23,000 × t)
Therefore, the formula to represent the value of the condo V(t), as a function of time t, where t is in years after 1977, is:
V(t) = $60,000 + ($23,000 × t)