If c is a linear function with c(0) = 5 and c(6) = 15, then c(9) = 20
The given parameters are:
c(0) = 5
c(6) = 15
That is, x₁ = 0, c₁ = 5, x₂ = 6, c₂ = 15
The slope of the linear function is calculated by the formula:
[tex]m=\frac{c_2-c_1}{x_2-x_1} \\\\[/tex]
Substitute x₁ = 0, c₁ = 5, x₂ = 6, c₂ = 15 into the formula:
[tex]m=\frac{15-5}{6-0} \\\\m= \frac{10}{6} \\\\m=\frac{5}{3}[/tex]
For c(9):
x₂ = 9, c₂ = ?
Substitute x₁ = 0, c₁ = 5 and m = 5/3 into the formula:
[tex]m=\frac{c_2-c_1}{x_2-x_1} \\\\[/tex]
[tex]\frac{5}{3}=\frac{c_2-5}{9-0} \\\\9(\frac{5}{3})= c_2 - 5\\\\15 = c_2 - 5\\\\c_2 = 15 + 5\\\\c_2 = 20[/tex]
Therefore, c(9) = 20
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