The function f(x) = 3e^-x represents the exponential decay of a unit of kryptonite in grams per year, where x is years. Using the graph you made, how many years (x) does it take for the kryptonite to be less than 0.055 grams?

Respuesta :

In order to answer the question, we have to solve the equation:
[tex]3e^{-x}\ \textless \ 0.055,\text{ divide by 3 like this:}\\e^{-x}\ \textless \ \frac{0.055}{3}\\e^{-x}\ \textless \ 0.018,\text{ apply the log function to the two sides of the inequality:}\\-x\ \textless \ \log(0.018)\\-x\ \textless \ -4,\text{ therefore:}\\x\ \textgreater \ 4[/tex]

So it take 4 years in order to the kryptonite to be less than 0.055 grams.