Chapter 9, Problem 1P

To determine

To write:

A MATLAB code to find the two solutions of the equation $x^3-e^{0.8x}=20$ between $x=0$ and $x=8$.

Answer to Problem 1P

Solution:

The two solutions of the equation $x^3-e^{0.8x}=20$ between $x=0$ and $x=8$ are $x_1=3.2082$ and $x_2=7.4898$.

Explanation of Solution

The given equation is,

$x^3-e^{0.8x}=20$

The value of $x$ lies between $x=0$ and $x=8$.

Solve the above equation to get the output,

$x_1=3.2082$

$x_2=7.4898$

Write the MATLAB code to find the two solutions of the equation $x^3-e^{0.8x}=20$ between $x=0$ and $x=8$.

MATLAB Code:

F = @(x)x^(3) - exp(0.8*x)-20;

fplot(F,[0 8])

fzero(F,0)

fzero(F,8)

Save the MATLAB script with name, Chapter9_56830_9_1P.m in the current folder. Execute the script by typing the script name at the command window to get the code to find the two solutions of the equation $x^3-e^{0.8x}=20$ between $x=0$ and $x=8$.

Result:

Conclusion:

Therefore, the two solutions of the equation $x^3-e^{0.8x}=20$ between $x=0$ and $x=8$ are $x_1=3.2082$ and $x_2=7.4898$.