An endangered frog species has a population of 10 000.

Question

An endangered frog species has a population of 10 000. Biologist estimate that the stock is decreasing at 3% per year. At this rate, approximately how many years will it take before only 80% of the species remains?

Answer 1

P(t) = P₀*(1 - r)^t

• P(t) = Population at time t = 80% of P₀ = 0.8P₀
• P0 = initial population = 10,000
• r = rate of decrease = 3% = 0.03
• t = years

 

P(t) = P₀*(1 - r)^t

0.8*(10,000) = (10,000)*(1 - 0.03)^t

0.8 = (0.97)^t

log(0.8) = log(0.97^t)

log(0.8) = t*log(0.97)            Log property: log(a^b) = b*log(a)

log(0.8)/log(0.97) = t

 

Use your calculator to get the answer.  You can use any base log.