Question

find the total income produced by a continuous income stream in the first 15 years if the rate of flow is given by the following function, where t is time in years.

f(t)=2500

how much was earned over 15 years? $\square$

Explanation:

Step1: Recall the formula for total income

The formula for the total income \(I\) from a continuous income stream with rate of flow \(f(t)\) over the interval \([a,b]\) is \(I=\int_{a}^{b}f(t)dt\). Here, \(a = 0\), \(b=15\), and \(f(t)=2500\).

Step2: Evaluate the integral

We know that \(\int_{0}^{15}2500dt\). Using the rule \(\int kdt=kt + C\) (where \(k\) is a constant), we have:

$$
LATEXBLOCK0
$$

Step3: Calculate the result

\(2500\times15=37500\)

Answer:

\(37500\)