exponential growth w/ constant ln(5)/10: how many days until

[tsh44]

Hi I would appreciate some help.

A container with a maximum capacity of 25,000 fruit flies intially contains 1000 fruit flies. If the population grows exponentially with a growth constant of ln(5)/10 fruit flies per day, in how many days will the container be full?

I have 25000= (ln(5)/10)^x *1000
25= (ln(5)/10)^x
ln25= x (ln(ln(5)/10)
x=-1.76

Does this mean the asner is 1.76 days?

 

[skeeter]

I do not think you have interpreted the growth constant correctly ...

in the natural exponential growth equation shown below, k is usually considered to be the growth constant.

\(\displaystyle \L P = P_o e^{kt}\)

\(\displaystyle \L P = 1000 e^{\frac{\ln{5}}{10}t} = 1000 \cdot 5^{\frac{t}{10}}\)

so ...

\(\displaystyle \L 25 = 5^{\frac{t}{10}}\)

t = 20 days