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

Question

asked Jun 11, 2023 42.3k views

1 Answer

Smarques · Answer 1 · 2023-06-15T09:59:40+0000

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)

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

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

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

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

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

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

$\Rightarrow {b} = 1.49379$

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