   Chapter 13, Problem 54RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Total income Suppose that a continuous income stream has an annual rate of flow f ( t ) = 100 e − 0.01 t 2 (in thousands of dollars per year). Use Simpsons Rule with n = 4 to approximate the total income from this stream over the next 2 years.

To determine

To calculate: The total income over the next 2 years by Simpson’s Rule with n=4. The continuous income stream has an annual flow rate f(t)=100e0.01t2.

Explanation

Given Information:

The continuous income stream has an annual flow rate f(t)=100e0.01t2 in thousands of dollars per year and the divisions n=4.

Formula Used:

Simpson’s Rule for a continuous function f(x) on the interval [a,b] which is divided into an even number n of equal subdivisions then,

abf(x)dxh3[f(x0)+4f(x1)+2f(x2)+4f(x3)++2f(xn2)+4f(xn1)+f(xn)]

Where, h=ban.

Calculation:

Consider the function, f(t)=100e0.01t2

The lower limit is 0 and for 2 years, the upper limit is 2.

So, a=0 and b=2.

Now, the value of h is,

h=ban

Substitute a=0, b=2 and n=4 in h=ban.

h=204=0.5

The values of t are,

t0t1t2t3t400.511.52

By Simpson’s rule,

02100e0

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