Answer: 909.03
Step-by-step explanation:
We know that the equation is an exponential function, it can be written as y=ab^x
[tex]100 &=a b^{6.5} \dots \mathrm{Equation \ 1} \\11 &= a b^{1} \\[/tex]
[tex]\Rightarrow ab^1=11[/tex]
[tex]\Rightarrow \frac{ab^1}{b}=\frac{11}{b};\quad \:b\ne \:0[/tex]
[tex]\Rightarrow a=\frac{11}{b}[/tex]
a = 11/b, substitute it in equation 1
[tex]100 &=a b^{6.5}[/tex]
[tex]\Rightarrow 100=\left(\frac{11}{b}\right)b^{6.5}[/tex]
[tex]\Rightarrow 100b=11b^\frac{11}{2}[/tex]
[tex]\Rightarrow 11\sqrt{b^{11} } =100b[/tex]
[tex]\Rightarrow \sqrt{b^{11} } =\frac{100}{11}}[/tex]
[tex]\Rightarrow \sqrt{b^{11} } =\frac{100}{11}}[/tex]
[tex]\Rightarrow {b^{11} } =\frac{10000}{121}}[/tex]
[tex]\Rightarrow {b} =\frac{\sqrt[11]{10000 \cdot 11^9} }{11}[/tex]
[tex]\Rightarrow {b} = 1.49379[/tex]
a = 11/b
a = 11/(1.49379)
a = 7.36382
Equation: y = (7.36382)(1.49379)^x
Now plug in 12 for x:
[tex]\Rightarrow { \left(7.36382\right)\left(1.49379\right)^{12}[/tex]
[tex]\Rightarrow 7.36382\cdot \:1.49379^{12}[/tex]
[tex]\Rightarrow 7.36382\cdot \:123.44530\dots[/tex]
[tex]\Rightarrow 909.03[/tex]
Therefore, f(12) = 909.03 for the exponential function
