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Answer:
Month 4
Step-by-step explanation:
To solve this problem we must propose an equation that models the number of kilometers of bicycle trails made monthly in Charles City and in Tinsel Town
<em>For Charles City </em>we know that the number of kilometers built in the first month is 5, and it doubles every month. Then we have an exponential equation, in base 2, whose initial value is 5.
This equation has the following form:
Where:
is the number of kilometers built in month 1
x is the number of months: {1, 2, 3, 4, 5 ... x}
x = 1 represents month 1.
So:
<em>For Tinsel Town</em> we know that the number of kilometers built in the first month is 21 and increases at a fixed rate of 5 kilometers per month. This can be modeled by a linear equation.
Where x is the number of months. x: {1, 2, 3, 4, 5 ...}
We want to know at the end of what month the total length of the cycle lanes in Charles City first exceeds the length in Tinsel Town
Then we equal both equations and clear x.
Clearing x from this equation is very difficult, so to find x, we iterate until we get the value of x that causes the equation to approach 0.
For x = 3
For x = 4
<em>The value must be between x = 3 and x = 4</em>
For x = 3.8
Then x ≈ 3.8 months.
Finally we have that By the end of the fourth month the total length of the cycle lanes in Charles City exceeds the length in Tinsel Town