A new apartment building was sold for $125000 4 years after it was purchased. The original owners calculated that the building appreciated $3000 per year while they owned it. Find a linear function that describes the appreciation of the building, if x is a number of years since the original purchase.
y = mx + b
y = new price of apartment
m = amount changed per year
x = change in time
b = starting price of apartment
it gives us one scenario, so solve for b:
125,000 = (3000)4 + b
b = 113,000
Therefore, the linear function associated with this is...
y = 3000x + 113000
Well, it seems like this building was quite the lucrative investment! Now, let's get down to the numbers.
We know that the building appreciated $3000 per year while it was owned by the original owners. So, we can start our linear function by saying that for each year, the value of the building increased by $3000.
But hold your laughter there, my dear friend! We need to also consider the initial value of the building when it was purchased. So, we need to add that to our function.
Let's call the original purchase price P and the number of years since the original purchase x. Therefore, our linear function that describes the appreciation of the building would be:
Appreciation(x) = 3000x + P
Now, since we already know that the building was sold for $125000 after 4 years, we can plug those values into our function to find P:
125000 = 3000(4) + P
Now it's time to do some calculations! Suit up, my fellow mathematician, and let's find P:
125000 = 12000 + P
P = 125000 - 12000
P = 113000
So, after some serious number crunching, we find that the initial purchase price of the building was $113000.
Therefore, our final linear function that describes the appreciation of the building would be:
Appreciation(x) = 3000x + 113000
Ta-da! The clown mathematician strikes again!
To find a linear function that describes the appreciation of the building, we can use the equation of a line.
Let's consider the initial purchase price as the starting point.
The initial purchase price is $125,000. Given that the building appreciates $3,000 per year, we can write the equation of the line as:
y = mx + b
where y represents the price of the building in dollars, x represents the number of years since the original purchase, m represents the rate of appreciation per year, and b represents the initial purchase price.
In this case, the rate of appreciation per year (m) is $3,000, and the initial purchase price (b) is $125,000. Therefore, the equation of the line describing the appreciation of the building is:
y = 3000x + 125000
This linear function shows the relationship between the number of years since the original purchase (x) and the price of the building (y) at that point in time.
To find a linear function that describes the appreciation of the building, we need to determine the equation in the form "y = mx + b", where "y" represents the value of the building after "x" years, "m" is the slope (rate of appreciation), and "b" is the initial value (original purchase price).
Given that the original owners calculated that the building appreciated $3000 per year, we can deduce that the slope (m) is $3000.
Now, let's find the initial value (b). We know that the building was sold for $125000 after 4 years. So, if we subtract the total appreciation from the final value, we can find the initial value.
Total appreciation in 4 years = $3000 * 4 = $12000
Final value = $125000
Initial value = Final value - Total appreciation = $125000 - $12000 = $113000
Therefore, the linear function that describes the appreciation of the building is:
y = 3000x + 113000
This equation represents the value of the building (y) after "x" years since the original purchase.