Question

The population of an endangered species is decreasing so that 90% of the population remains after the passage of one year. If there are 320 individuals at the beginning of a
study, then the function P = 320 (0.9)t gives the population at any time,t.
(a) Make a table showing the population at the end of years 1,2,3 and 4.
i got 288, 259,233,210
(b) In how many years will the population be reduced to 100 individuals?
i set up the equation as 100=320(.9)^t
i know that the answer is 11 but i can't seem to get the right answer.

Answer 1

for (a) you should round off 259 to 260 and 233 to 234...after all there's no "half" animal

for (b)

\[100 = 320 (0.9)^t\]
\[\frac{100}{320} = 0.9^t\]
\[\ln (\frac{100}{320}) = t\ln (0.9)\]
\[\frac{\ln (\frac{100}{320})}{\ln (0.9)} = t\]
that should give you 11

Answer 2

thank you my mistake was not doing the ln

Answer 3

ahh i see. hope you learned your mistake :)