Step-by-step explanation:
arctan(x) is less than π/2 for x > 0. Therefore, if we say g(x) = 13 (π/2) / eˣ, then f(x) < g(x) for all values of x > 0.
g(x) = 13 (π/2) / eˣ
g(x) = 13π/2 · (1/e)ˣ
So g(x) is a geometric series where r = 1/e. Since |r| < 1, the series converges.
Since g(x) converges, the smaller f(x) also converges.
So we know 20% of the audience are teenagers, and there are 360 teenagers.
Therefore, 1/5 of the audience members were teenagers, and that means 1/5 of the audience members is 360.
Multiply it by 5 to get answer:
360 * 5 = 1800
The total number of audience members are 1800.
Whats the balance for five years??
6 · e^(4x - 2) = 3
e^(4x - 2) = .5
ln e^(4x - 2) = ln (.5)
4x - 2 = ln (.5)
4x = ln (.5) + 2
x = (ln (.5) + 2)/4
x = 0.3267
x ≈ 0.327
Answer: B
