I have no idea how to set up this problem. I am aware of the formula $$A = Pe^{rt}$$ Assume the cost of a gallon of milk is $2.90. With continuous compounding, find the time it would take the cost to be 5 times as much (to the nearest tenth of a year), at an annual inflation rate of 6%.
I also know that the 6% goes in for the r (rate) as such
$$A = Pe^{.06t}$$
On
You can use $A=Pe^{rt}$ if you want. But then we have to find $r$. In one year, the price goes from $1$ to $1.06$, so $1.06=e^r$, giving $r=\ln(1.06)$. Now continue.
Alternately, use the equation $A=P(1.06)^t$. Let $q$ be the amount of time it takes for the price to quintuple. Put $A=5P$. Then we are solving the equation $(1.06)^q=5$. Take the logarithm of both sides, preferably the natural logarithm. We get $$q\ln(1.06)=\ln(5),$$ and now $q$ is easy to find.
You don't actually care what the current cost is. You are asked to find the $t$ that corresponds to $\frac AP=5$, which is when the price of anything has been multiplied by $5$. Your equation $A=Pe^{0.06t}$ gives an annual rate higher than $6\%$-plug in $t=1$ to get $\frac AP\approx 1.0618$ for a annual rate of $6.18\%$