the function f(x)= 34.1 Ln x + 117.7
models the number of U.S. Internet users, f(x) in millions, x years after 1999. By which year will there be 250 million Internet users in the U.S.?
just solve
34.1 lnx + 117.7 = 250
34.1 lnx = 132.3
lnx = 3.88
x = 48.4
so, we're looking at 2048
To find the year when there will be 250 million Internet users in the U.S., we need to solve the equation f(x) = 250. The function f(x) represents the number of U.S. Internet users in millions, x years after 1999.
The given function is:
f(x) = 34.1 Ln x + 117.7
Let's substitute the value of f(x) as 250 and solve for x:
250 = 34.1 Ln x + 117.7
First, subtract 117.7 from both sides of the equation:
250 - 117.7 = 34.1 Ln x
132.3 = 34.1 Ln x
Next, divide both sides of the equation by 34.1:
Ln x = 132.3 / 34.1
Ln x ≈ 3.88
Now, to find x, we need to take the exponential of both sides of the equation using the inverse of the natural logarithm (e):
x = e^(Ln x)
x ≈ e^3.88
Using a calculator or computer software, we can find that e^3.88 is approximately 48.80.
Thus, x is approximately 48.80 years after 1999.
To find the year, we add 48.80 to 1999:
1999 + 48.80 ≈ 2047.80
Therefore, by approximately the year 2048, there will be 250 million Internet users in the U.S.