Old Farmer MacDonald wants to build a pen to keep his chickens in. He has 36 meters of fence and plans to make a rectangular pen
. Complete the chart to help Old MacDonald decide how to make his chicken pen so that he has the maximum area.
1 answer:
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So, the value of x is 1.19
The question is an exponential equation
<h3>What is an exponential equation?</h3>An exponential equation is a mathematical expression between two quantities in which one variable is raised to a power of the other variable.
<h3>How to find x?</h3>
Since ,
Dividing through by 4ˣ, we have
Let y = (3/2)ˣ
So,
1 + y = y²
y² - y - 1 = 0
Using the quadratic formula to find y,
where a = 1 b = -1 and c = -1
Substituting the values of the variables into the equation, we have
Since y = (3/2)ˣ
Takung logarithm of both sides, we have
㏒y = ㏒(3/2)ˣ
㏒y = x㏒(3/2)
x = ㏒y/㏒(3/2)
x = ㏒y/㏒1.5
Since we do not have logarithm of a negative number, we use y = 1.618.
So, x = ㏒y/㏒1.5
x = ㏒1.618/㏒1.5
x = 0.2090/0.1761
x = 1.19
So, the value of x is 1.19
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