The size of the coyote population at a national park increases at the rate of 4.6% per year. If the size of the current population is 130, find how many coyotes there should be in 6 years. Use the function f(x)=130e^0.046t
so, just plug in 6 for t.
To find the number of coyotes in 6 years, we can use the function f(x) = 130e^(0.046t), where t represents the number of years.
Substituting t = 6 into the function:
f(6) = 130e^(0.046 * 6)
To calculate this expression, we need to use the exponential function e^x. The value of e is approximately 2.71828.
f(6) = 130e^(0.276)
f(6) ≈ 130 * 2.71828^(0.276)
f(6) ≈ 130 * 1.317780
f(6) ≈ 171.212
Therefore, there should be approximately 171 coyotes in the national park after 6 years.
To find the number of coyotes there should be in 6 years, we can use the exponential growth formula:
f(x) = a * e^(r*t)
Where:
f(x) represents the future value of the population (number of coyotes after x years),
a represents the initial value of the population (current population),
e is Euler's number (approximately 2.71828),
r represents the growth rate as a decimal (4.6% = 0.046),
and t represents the number of years in the future.
In this case, the current population (a) is 130, the growth rate (r) is 0.046, and we want to find the population in 6 years (t = 6). Plugging these values into the formula, we get:
f(6) = 130 * e^(0.046 * 6)
To solve this mathematically, we can use a calculator or an online tool that supports exponentials. Evaluating the expression, we find:
f(6) ≈ 130 * e^(0.276) ≈ 130 * 1.31812 ≈ 171.254
Therefore, there should be approximately 171 coyotes in the national park after 6 years.