I am not sure how to solve these problems :( can I get some help please?

Question

1354 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-06T00:07:27

4 years old

This requires solving equations with logarithms:

$P (x) = 31 = \frac{90}{1 + 271 e^{- 0.122 x}}$ $P(x)=31=90/(1+271e^(-0.122x))$ and we want to solve for $x$ $x$

Rewriting:

$1 + 271 e^{- 0.122 x} = \frac{90}{31}$ $1+271e^(-0.122x)=90/31$

$e^{- 0.122 x} = \frac{\frac{90}{31} - 1}{271}$ $e^(-0.122x)=(90/31-1)/271$

$e^{- 0.122 x} = \frac{59}{8401}$ $e^(-0.122x)=59/8401$

Take the natural logarithm of both sides:

$ln (e^{- 0.122 x}) = ln (\frac{59}{8401})$ $ln(e^(-0.122x))=ln(59/8401)$

$- 0.122 x = ln (\frac{59}{8401})$ $-0.122x=ln(59/8401)$

$x = \frac{ln (\frac{59}{8401})}{- 1.22}$ $x=(ln(59/8401))/-1.22$

$x = 4.06$ $x=4.06$

Rounded to a whole number would be 4 years old.