I am trying to solve the question:
A population of protozoa develops with a constant relative growth rate of 0.7944 per member per day. On day zero, the population consists of two members. Find the population size after six days.
I used 2 different methods to solve the problem, and each method gave a different answer.
First method:
$\frac{dP}{dt}=0.7944P\\ \Rightarrow P_t=Ce^{0.7944t}\\ P_0=2=C\\ P_6=2e^{0.7944\times6}\approx 235$
$\text{}$
Second method:
$A=P(1+r)^n\\ A=2(1.7944)^6\approx 67$
$\text{}$
Which method is correct?
I finally confirmed that the solution is 235. So your first method is true. According to this and this relative growth rate (RGR) is also calculated with the following formula:
$$RGR=(\ln{P_1}-\ln{P_0})/(t_1-t_0)$$
where $t_1$ and $t_0$ are time in days and $P_1$ and $P_2$ are population. If you put:
$$0.7944=\frac{\ln{}P-ln2}{6}$$
You find:
$$P\approx235$$