Zoology. The number of snails, n, in a colony after t weeks obeys the formula n=20e^0.1t.

Find, giving your answer to the nearest integer:

the least number of weeks needed for the number of snails to exceed 200.

right so i subbed in the 200 to n and then logged it to find t, but i can't seem to get the correct answer. Here is my working, if you can tell me what went wrong with it..

200=20e^0.1t
ln200=ln20e^0.1t
ln200=ln20+lne^0.1t
ln200/ln20=(0.1t)logbase(e)
ln200/ln20=0.1t(1)
ln200/ln20=0.1t

and then i divided ln200/ln20 by 0.1 to get t... but somehow its not the answer.

Question

Zoology. The number of snails, n, in a colony after t weeks obeys the formula n=20e^0.1t.

Find, giving your answer to the nearest integer:

the least number of weeks needed for the number of snails to exceed 200.

right so i subbed in the 200 to n and then logged it to find t, but i can't seem to get the correct answer. Here is my working, if you can tell me what went wrong with it..

200=20e^0.1t
ln200=ln20e^0.1t
ln200=ln20+lne^0.1t
ln200/ln20=(0.1t)logbase(e)
ln200/ln20=0.1t(1)
ln200/ln20=0.1t

and then i divided ln200/ln20 by 0.1 to get t... but somehow its not the answer.

imstuck · Answer

If the population exceeds 200, then the number to the left of the equals sign cannot be 200, it has to be greater than 200.  I did 201=20e^.1t and got the number of weeks to be 23.

anonymous · Answer

ahhh okay

but 23? you rounded up or down?