The size of the beaver population at a national park increases at the rate of 4.3% per year. If the size of the current population is 142, find how many beaver there should be in 4 years. Use the function f(x)=4e^0.043t and round to the nearest whole number
just replace t with 4 and evaluate, using your calculator
population = 4 e^(.043(4))
= ....
I think your function should have been
f(t) = 142 e^(.043t)
check your typing
To find the estimated beaver population after 4 years, we can use the formula f(x) = 142 * e^(0.043 * 4).
Let's calculate it step by step:
Step 1: Calculate the exponent.
0.043 * 4 = 0.172
Step 2: Calculate the value of e raised to the exponent.
e^0.172 ≈ 1.186
Step 3: Multiply the result by the initial population.
142 * 1.186 = 168.412
Step 4: Round the result to the nearest whole number.
Rounding 168.412 to the nearest whole number, we get 168.
Therefore, after 4 years, the estimated beaver population should be 168.
To find out how many beavers there should be in 4 years, we can use the exponential growth function given: f(x) = 4e^0.043t, where t represents the time in years.
First, let's substitute t = 4 into the function:
f(4) = 4e^(0.043 * 4)
Next, we need to evaluate e^(0.043 * 4):
e^(0.043 * 4) = e^(0.172)
Now, we can calculate the value of e^(0.172):
e^(0.172) = 1.1875 (rounded to four decimal places)
Finally, we multiply the result by the current population size of 142:
f(4) = 4 * 1.1875 * 142
f(4) ≈ 845.75
Rounding to the nearest whole number, there should be approximately 846 beavers in 4 years.