The number y of daily fee golf facilities in the United States from 1995 to 2003 can be represented by the following model where t represents the year with t = 5 corresponding to 1995.
y=4381+1883.6lnt
5=t=13
During which year did the number of daily fee golf facilities reach 9000?
2001
To find the year when the number of daily fee golf facilities reached 9000, we need to solve the given equation for t (year) using the provided formula:
y = 4381 + 1883.6 * ln(t)
Let's substitute y = 9000 into the equation and solve for t:
9000 = 4381 + 1883.6 * ln(t)
Subtracting 4381 from both sides:
9000 - 4381 = 1883.6 * ln(t)
4619 = 1883.6 * ln(t)
Dividing both sides by 1883.6:
2.45 = ln(t)
We can solve for t (year) by taking the exponential of both sides:
e^2.45 = e^(ln(t))
e^2.45 = t
Using a calculator, we can find that e^2.45 is approximately 11.564.
So, the number of daily fee golf facilities reached 9000 in the year t ≈ 11.564. Since t corresponds to the year 1995 + t, we can calculate the year:
t = 11.564 ≈ 12
Therefore, the number of daily fee golf facilities reached 9000 approximately during the year 1995 + 12 = 2007.
To find the year when the number of daily fee golf facilities reached 9000, we need to solve the equation y = 9000.
The equation given is y = 4381 + 1883.6 * ln(t).
We can substitute y with 9000 and solve for t:
9000 = 4381 + 1883.6 * ln(t)
Subtracting 4381 from both sides:
9000 - 4381 = 1883.6 * ln(t)
4619 = 1883.6 * ln(t)
Dividing both sides by 1883.6:
4619 / 1883.6 = ln(t)
2.45 = ln(t)
To solve for t, we need to exponentiate both sides using the natural exponential function (e):
e^2.45 = e^ln(t)
e^2.45 ≈ 11.569
Therefore, t ≈ 11.569.
Since t represents the year with t = 5 corresponding to 1995, we need to add 5 to the calculated value of t:
Year = 11.569 + 5 ≈ 16.569
Rounding the year to the nearest whole number, the number of daily fee golf facilities reached 9000 around the year 17.
Therefore, the answer is that the number of daily fee golf facilities reached 9000 in the year 2012.