Question

Can someone find F(12).
i really have no idea...
Please and thank you?

Answer 1

Answer: 909.03

Explanation:

We know that the equation is an exponential function, it can be written as y=ab^x

`100 &=a b^(6.5) \dots \mathrm{Equation \ 1} \\11 &= a b^(1) \\`

`\Rightarrow ab^1=11`

`\Rightarrow (ab^1)/(b)=(11)/(b);\quad \:b\\e \:0`

`\Rightarrow a=(11)/(b)`

a = 11/b, substitute it in equation 1

`100 &=a b^(6.5)`

`\Rightarrow 100=\left((11)/(b)\right)b^(6.5)`

`\Rightarrow 100b=11b^(11)/(2)`

`\Rightarrow 11\sqrt{b^(11) } =100b`

`\Rightarrow \sqrt{b^(11) } =(100)/(11)}`

`\Rightarrow \sqrt{b^(11) } =(100)/(11)}`

`\Rightarrow {b^(11) } =(10000)/(121)}`

`\Rightarrow {b} =\frac{\sqrt[11]{10000 \cdot 11^9} }{11}`

`\Rightarrow {b} = 1.49379`

a = 11/b

a = 11/(1.49379)

a = 7.36382

Equation: y = (7.36382)(1.49379)^x

Now plug in 12 for x:

`\Rightarrow { \left(7.36382\right)\left(1.49379\right)^(12)`

`\Rightarrow 7.36382\cdot \:1.49379^(12)`

`\Rightarrow 7.36382\cdot \:123.44530\dots`

`\Rightarrow 909.03`

Therefore, f(12) = 909.03 for the exponential function