Need help solving

There are originally 1000 bacteria in a culture, and 4 hours later there are 4000. Find the rate of increase per hour of the bacteria.

(Please do not use logs for this problem. I need the most basic way to do it with exponential growth.)

Question

Need help solving 

There are originally 1000 bacteria in a culture, and 4 hours later there are 4000. Find the rate of increase per hour of the bacteria. 

(Please do not use logs for this problem. I need the most basic way to do it with exponential growth.)

calculusxy · Answer

Should I use the formula: $y = ab^x$?

jdoe0001 · Answer

sure $\begin{array}{llrll}
originally&1000&y = 1000(b)^o\
4hrs\ later&4000& y =1000(b)^x\
&&4000=1000(b)^4\
&&\cfrac{\cancel{4000}}{\cancel{1000}}=b^4\
&&4=b^4\
&&\sqrt[4]{4}=b
\end{array}$

calculusxy · Answer

That's what I did and got the answer of $\approx$ 1.41. But the answer key says that the answer is 0.3467.

jdoe0001 · Answer

$\bf 1000( 0.3467)^4\approx 14.44$

jdoe0001 · Answer

not even close btw, so... can't be 0.3467

jdoe0001 · Answer

now if you plug your 1.41, you'll get a workable number
now, if you use 1.4142135623730950488  , you'll get pretty much 3999.99999999

calculusxy · Answer

That's what the answer key says. I tried it out with the formula of $\large A = Pe^{r(t)}$ and it was 0.3467. But my teacher thinks that it would be too advanced to use that formula does not want me to use it. What can I do as an alternative?

jdoe0001 · Answer

well, it doesn't fit for the equation of $\bf y = 1000(b)^x$ though, 1.41 does

jdoe0001 · Answer

or to be exact, 1.4142135623730950488 =)