If 25 individuals were alive in 1955 and 500 existed in 2013, what is r?
Show work please!
a) 475
b)2.99
c)0.052
d)0.029
0.052
To find the value of r, we can use the formula for exponential growth:
N = N₀ * (1 + r)^t
Where:
N is the final population,
N₀ is the initial population,
r is the growth rate,
t is the time in years.
In this case, we know that in 1955 there were 25 individuals (N₀), and in 2013 there were 500 individuals (N). The difference in time between these two years is 2013 - 1955 = 58 years.
Plugging in the values we know into the formula, we get:
500 = 25 * (1 + r)^58
Now we can start solving for r.
Divide both sides of the equation by 25:
(500 / 25) = (1 + r)^58
Simplify the left side:
20 = (1 + r)^58
Take the 58th root of both sides to isolate (1 + r):
(20)^(1/58) = 1 + r
Now subtract 1 from both sides:
(20)^(1/58) - 1 = r
Using a calculator, we can find that (20)^(1/58) is approximately 1.0299.
So, r ≈ 1.0299 - 1 ≈ 0.0299.
Therefore, the answer is approximately 0.029, which corresponds to option d) in the given choices.