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 of deer in the state after 5 years, we can use the formula for compound interest. In this case, the population growth can be considered as compound interest.

Let's break it down step-by-step:

Step 1: Define the given variables:
Initial population (P) = 10,280
Annual growth rate (r) = 1% = 0.01 (expressed as a decimal)
Number of years (t) = 5

Step 2: Calculate the population after 5 years using the formula:
Population after t years (A) = P × (1 + r)^t

Step 3: Substitute the values into the formula:
A = 10,280 × (1 + 0.01)^5

Step 4: Simplify the equation:
A = 10,280 × (1.01)^5

Step 5: Use a calculator to evaluate the expression:
A ≈ 10,280 × 1.05101005

Step 6: Calculate the population after 5 years:
A ≈ 10,834.95 (rounded to the nearest whole number)

Therefore, the predicted population of deer in the state after 5 years is approximately 10,835.

To predict the population of deer after 5 years, we need to calculate the population growth annually and then compound it over the given period.

The annual growth rate is given as 1%. This means that every year, the population will increase by 1% of its current value.

To calculate the population after 1 year, we can use the formula:
Population after 1 year = Initial population + (Initial population * Growth rate)

Plugging in the given values:
Population after 1 year = 10,280 + (10,280 * 0.01) = 10,280 + 102.8 = 10,382.8

Now, we need to repeat this process for each subsequent year. The population after 2 years will be the population after 1 year plus the growth from the second year:
Population after 2 years = Population after 1 year + (Population after 1 year * Growth rate)

Population after 2 years = 10,382.8 + (10,382.8 * 0.01) = 10,382.8 + 103.828 = 10,486.628

Similarly, we can calculate the population after 3 years, 4 years, and finally 5 years by using the same formula:

Population after 3 years = 10,486.628 + (10,486.628 * 0.01) = 10,486.628 + 104.86628 = 10,591.49428

Population after 4 years = 10,591.49428 + (10,591.49428 * 0.01) = 10,591.49428 + 105.9149428 = 10,697.4092228

Population after 5 years = 10,697.4092228 + (10,697.4092228 * 0.01) = 10,697.4092228 + 106.974092228 = 10,804.383315028

Therefore, the predicted deer population after 5 years would be approximately 10,804.38.

10280 * 1.01^5