A population is increasing according to the exponential function defined by y = 2e0.02x, where y is in millions and x is the number of years. How large will the population be in 3 years?
what's the problem? plug in 3 for x:
y = 2e^0.06 = 2.12
Well, since the function is y = 2e0.02x, let's plug in x = 3 and see what happens.
So, when x = 3, we have y = 2e0.02(3).
To simplify this, we calculate that 0.02(3) = 0.06. So now we have y = 2e0.06.
Now, we just need to use our good friend, Mr. Calculator, to evaluate e0.06.
After doing some calculations, we find that e0.06 is approximately equal to 1.0618 (or some other number equally as fun).
So, multiplying 2 by 1.0618, we find that the population will be approximately 2.1236 million (or a few clowns short of a circus) in 3 years.
To determine how large the population will be in 3 years, we can substitute the value of x = 3 into the given exponential function:
y = 2e^(0.02x)
Substituting x = 3:
y = 2e^(0.02 * 3)
First, we calculate 0.02 * 3:
0.02 * 3 = 0.06
Next, we substitute this value back into the equation:
y = 2e^(0.06)
Now, let's find the value of e^(0.06) using a calculator:
e^(0.06) ≈ 1.061836546
Finally, we substitute this value back into the equation:
y = 2 * 1.061836546
y ≈ 2.123673092
Therefore, the population will be approximately 2.1 million in 3 years.
To find the population after 3 years, you need to substitute the value of x = 3 into the given exponential function y = 2e0.02x.
Step 1: Substitute x = 3 into the exponential function.
y = 2e0.02(3)
Step 2: Simplify the expression inside the exponential.
y = 2e0.06
Step 3: Evaluate the exponential expression.
y ≈ 2(1.061837) [Using the approximation e ≈ 2.71828]
y ≈ 2.123674
So, the population will be approximately 2.123674 million in 3 years.