I am reviewing algebra 2 and stuck with this question.
The population P of a city is given by
p = 25000e^kt
where t is the time in years, with t = 0 corresponding to the year 1990. In 1945, the population was 3,350. Find the value of k.
The solution proposed by my prof looks like this:
3350 = 25000e^k(-45)
My question is why is there a negative sign in front of 45.
Is that because the population is decreasing (i.e. exponential decay)?
Year $t=0$ is $1990$. The other year you know about ($1945$) is in the past. Looking backwards in time looks like decay. If you solve the equation you've written you will get a positive $k$. It's $t$ that's negative.