The size of the beaver population at a national park increases at the rate of 5.1% per year. If the size of the current population is 151, find how many beavers there should be in 4 years. Use the function f(x)=151e^0.051t and round to the nearest whole number. (This is what I got so far: f(4)=151e^0.051t, would I then have to divide each side by e?)
No
first of all the function should say
f(t)=151e^0.051t and not f(x)=151e^0.051t
replace the t with 4 and you get
f(4)=151e^0.051(4)
= 151e^.204
= 185
(on your calculator you should have a function called e^x, usually found as the inverse or second function of the "ln" key.
on my calculator I pressed "shift" then "ln" then .204 then = to get 1.2262..
which I then multiplied by 151)
To find the number of beavers in 4 years using the given function f(x) = 151 * e^(0.051 * t), where t represents the number of years, you need to substitute t with 4 and evaluate the expression.
f(4) = 151 * e^(0.051 * 4)
First, calculate the exponent part: e^(0.051 * 4)
e^(0.051 * 4) ≈ 1.221402758
Now, substitute the value of the exponent into the equation: f(4) = 151 * 1.221402758
Next, multiply: f(4) ≈ 184.55
Lastly, round the result to the nearest whole number: f(4) ≈ 185
Therefore, there should be approximately 185 beavers in the national park after 4 years.
To find the number of beavers in 4 years, you can use the population growth function:
f(t) = 151e^(0.051t)
where t is the number of years.
To find f(4), you substitute t = 4 into the equation:
f(4) = 151e^(0.051(4))
Now, to evaluate this expression, let's break it down step by step:
1. Calculate 0.051(4):
0.051 * 4 = 0.204
2. Substitute this result back into the equation:
f(4) = 151e^(0.204)
3. Evaluate the exponent (0.204) using the constant e = 2.71828:
e^(0.204) ≈ 1.2261
4. Multiply this result by 151:
f(4) ≈ 151 * 1.2261 ≈ 183.896
5. Round the final answer to the nearest whole number:
f(4) ≈ 184
Therefore, there should be approximately 184 beavers in the national park after 4 years.