The caribou population of an area has been growing at an annual rate of 2% ,
A) If there are 850 initially, how long before there is a 1000?
B)How long for it to double?
x
1000=850(1.02)
See previous post.
To answer these questions, we can use the formula for calculating exponential growth:
A = P(1 + r)^n
Where:
A = Final population
P = Initial population
r = Annual growth rate (as a decimal)
n = Number of years
Now let's analyze each question separately.
A) How long before the caribou population reaches 1000?
We have the initial population (P) as 850, the final population (A) as 1000, and the growth rate (r) as 2% or 0.02.
Plugging these values into the formula, we have:
1000 = 850(1 + 0.02)^n
To find the value of n, we need to isolate it. Divide both sides by 850:
1000/850 = (1 + 0.02)^n
Now take the logarithm of both sides:
log(1000/850) = n * log(1 + 0.02)
Using properties of logarithms, we can simplify:
log(1000/850) = n * 0.02
Finally, divide both sides by 0.02 to solve for n:
n = log(1000/850) / 0.02
Now, you can use a calculator or any logarithm-solving tool to calculate the value of n, which will give you the number of years it will take for the population to reach 1000.
B) How long for the population to double?
In this case, we want to find the time it takes for the population to grow by a factor of 2, which means the final population (A) will be twice the initial population (P).
Using the same formula, we have:
2P = P(1 + 0.02)^n
Dividing both sides by P, we get:
2 = (1 + 0.02)^n
Again, take the logarithm of both sides:
log(2) = n * log(1 + 0.02)
Simplifying:
n = log(2) / log(1 + 0.02)
Calculate the value of n using a calculator or logarithm-solving tool to determine how long it will take for the population to double.
Remember to round your answers to the nearest whole number since you can't have fractions or decimals for the number of years.