Question

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?

Answer 1

In order to answer the question, we have to solve the equation:

`3e^(-x)\ \textless \ 0.055,\text{ divide by 3 like this:}\\e^(-x)\ \textless \ (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`

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