In the year 2002, the rent in Chamomile Town was $1130, and it increases by 1.85% per year. Write a function f(t) for the rent in Chamomile City t years after 2002.
The average monthly rent in Lavender Town is also growing exponentially.
In the year 2010, the rent in Lavender Town was $250 less than the rent in Chamomile Town. In the year 2018, the rent in Lavender Town is $1500.
Write a function g(t) for the rent in Lavender Town t years after 2002.
f(t) = 1130 * 1.0185^t
f(8) = 1308.48, so
g(8) = 1058.48
g(0) = 1058.48 * (1+r)^-8
g(16) = g(0) * (1+r)^14 = 1500
so, 1058.58 * (1+r)^6 = 1500
r = 0.0598
g(0) = 665.17
g(t) = 665.17 * 1.0598^t
oops. I see a typo. fix it and redo the last few steps.
To write a function for the rent in Chamomile Town t years after 2002, we can use the given information that the rent increases by 1.85% per year.
Let's break down the problem step by step:
1. Calculate the annual increase:
- The rent increases by 1.85% per year, which is equivalent to multiplying it by 0.0185 (1.85% = 0.0185).
- We can express the annual increase as a percentage by adding 100% (1): 1 + 0.0185 = 1.0185.
2. Calculate the rent for a specific year:
- We start with the initial rent in 2002, which is $1130.
- To calculate the rent t years after 2002, we need to multiply the initial rent by the annual increase raised to the power of t: Rent(t) = $1130 * (1.0185)^t.
Therefore, the function f(t) that represents the rent in Chamomile Town t years after 2002 is:
f(t) = $1130 * (1.0185)^t
Now, you can substitute any value for t into the function to calculate the rent for a specific year.