Question

A small brewery considers the output of its bottling machine as a continuous income stream with an annual rate of flow at time t given by f(t)=90e−0.1t in thousands of dollars per year. Find the income from this stream for the next 10 years.

Answer 1

The question asks for the total income over 10 years from a continuous income stream given by the function f(t)=90e−0.1t. The solution involves setting up and evaluating the definite integral of this function from t=0 to t=10.

Step-by-step explanation:

The question involves calculating the total income from a continuous income stream over a 10-year period. The income stream is defined by the function f(t)=90e−0.1t, which represents thousands of dollars per year. To find the total income over the next 10 years, we need to integrate this function from t=0 to t=10.

Steps for Calculation:

1. Set up the integral of the function f(t) = 90e−0.1t from 0 to 10.
2. Apply the rules of integration to solve the integral.
3. Interpret the result to find the total income.

By calculating the definite integral, we will determine the area under the curve of this function, which in this context represents the total income stream over the specified time period.