Suppose the population of deer in a state is 10,280 and is growing 1% each year. Predict the population after 5 years
To predict the population after 5 years, we can use the formula for exponential growth:
P = P0 * (1 + r)^n
Where:
P = future population
P0 = initial population
r = growth rate (as a decimal)
n = number of years
Given:
P0 = 10,280
r = 1% = 0.01 (as a decimal)
n = 5
Calculating the population after 5 years:
P = 10,280 * (1 + 0.01)^5
Step 1: Calculate (1 + 0.01)^5
(1 + 0.01) = 1.01
(1.01)^5 ≈ 1.0510
Step 2: Multiply 10,280 by 1.0510
P ≈ 10,280 * 1.0510
P ≈ 10,803.63
The predicted population of deer after 5 years is approximately 10,803.
To predict the population of deer after 5 years, we can use the formula for exponential growth:
\[ P = P_0 \times (1 + r)^n \]
Where:
P = Population after n years
P₀ = Initial population
r = Annual growth rate (expressed as a decimal)
n = Number of years
In this case, the initial population (P₀) is 10,280, the annual growth rate (r) is 1% (or 0.01 as a decimal), and we want to find the population after 5 years (n = 5).
Substituting the values into the formula, we have:
\[ P = 10,280 \times (1 + 0.01)^5 \]
Calculating this expression will give us the predicted population of deer after 5 years.