There is a drought and the oak tree population is decreasing at the rate of 5% per year. If the population continues to decrease
at the same rate, how long will it take for the population to be half of what it is? If necessary, round your answer to the nearest tenth. The population will reach half of its original value in approximately ______ years.
The multiplier of the population each year is 5% less than 1, so is 0.95. Then the population in t years is multiplied by 0.95^t. We want to find t such that this value is 1/2.
0.50 = 0.95^t
log(0.50) = t·log(0.95)
log(0.50)/log(0.95) = t ≈ 13.5134 ≈ 13.5
The population will decline to half its original value in approximately 13.5 years.
