The revenue of a company represents the income generated by the company within a time frame. The total revenue generated by the company from the start of 2010 to the start of 2016 is $39.16 billion
Given that:
[tex]f(t) = 348e^{0.22t}[/tex] [tex]10 \le t \le 16[/tex]
First, we calculate the integral
[tex]\int\limits^{16}_{10} {f(t)} \, dt[/tex]
This is calculated as:
[tex]\int\limits^{16}_{10} {f(t)} \, dt = \int\limits^{16}_{10} {348e^{0.22t}} \, dt[/tex]
Remove the constant
[tex]\int\limits^{16}_{10} {f(t)} \, dt = 348\int\limits^{16}_{10} {e^{0.22t}} \, dt[/tex]
Now, integrate
[tex]\int\limits^{16}_{10} {f(t)} \, dt = 348 \times \frac{1}{0.22} (e^{0.22t})|\limits^{16}_{10}[/tex]
[tex]\int\limits^{16}_{10} {f(t)} \, dt = \frac{ 348}{0.22} (e^{0.22t})|\limits^{16}_{10}[/tex]
Expand
[tex]\int\limits^{16}_{10} {f(t)} \, dt = \frac{ 348}{0.22} (e^{0.22\times 16} -e^{0.22\times 10} )[/tex]
[tex]\int\limits^{16}_{10} {f(t)} \, dt = \frac{ 348}{0.22} (e^{3.52} -e^{2.2} )[/tex]
[tex]\int\limits^{16}_{10} {f(t)} \, dt = \frac{ 348}{0.22} \times 24.759[/tex]
[tex]\int\limits^{16}_{10} {f(t)} \, dt = 39164.2[/tex]
From the question
[tex]t = 10[/tex] represents the start of 2010.
This means that
[tex]t = 16[/tex] represents the start of 2016.
So, the interpretation is:
The total revenue from the start of 2010 to the start of 2016 is $39.16 billion
Read more about revenues at:
https://brainly.com/question/376674
