1.) 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.
2.) 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.
pls someone help i'm stuck on this and it's urgent
impatient much?
posting it again will not elicit any quicker response, and is just annoying.
1.) To write a function f(t) for the rent in Chamomile Town t years after 2002, we can use the formula for compound interest:
Rent = Initial Rent * (1 + Rate)^Years
In this case, the initial rent in 2002 is $1130, and it increases by 1.85% per year. So, the rate can be expressed as 0.0185.
Therefore, the function f(t) would be:
f(t) = 1130 * (1 + 0.0185)^t
2.) To write a function g(t) for the rent in Lavender Town t years after 2002, we need to consider the given information that in 2010, the rent in Lavender Town was $250 less than the rent in Chamomile Town.
Let's first find the rent in Chamomile Town in 2010 by using the function f(t) from the previous part.
For t = 2010 - 2002 = 8 years:
f(8) = 1130 * (1 + 0.0185)^8
Now, we subtract $250 from the rent in Chamomile Town in 2010 to get the rent in Lavender Town in 2010.
Rent in Lavender Town in 2010 = f(8) - $250
Since the rent in Lavender Town increases exponentially, we can write the function g(t) as:
g(t) = (f(t) - f(8)) + $1500
Combining the above equations, the final function g(t) for the rent in Lavender Town t years after 2002 would be:
g(t) = (1130 * (1 + 0.0185)^t - 1130 * (1 + 0.0185)^8) + $1500