A population of fruit flies starts with 6 flies. On Day 4, the population has grown to 94 flies. Wrote an exponential growth function to mod

We have.....

Pt = Pb^t-1     where P is the original population ....   Pt is the popoulation after "n" days  ... b is the growth rate... and t is the number of days ...[ t = 1 is the first day.....so, we're looking for the population 3 days after. the first day = the end of the 4th day ]....and we have

94 = 6b^{(4 - 1)}   =    6b⁽³⁾      divide both sides by 6

(94/6)  = b³        take the cube root of both sides

b ≈ 2.5022

So, our function is  :     Pn =   6(2.5022)^{(t - 1)}

Would it be reasonable for me to do it like this?

A population of fruit flies starts with 6 flies. On Day 4, the population has grown to 94 flies. Write an exponential growth function to model the growth of the fly population.

$$\\P=6e^{k(t-1)}\\\\
94=6e^{3k}\\\\
15.\dot6 = e^{3k} \\\\
ln(15.\bar6 )= ln(e^{3k}) \\\\
ln(15.\bar6 )= 3k \\\\
k=ln(15.\bar6 )/3 \\\\
k\approx 0.91718\\\\
so\\\\
P=6e^{0.91718(t-1)}\\\\$$

Is that ok?