F(x)=2^x+6
let f(x) = n
f^-1(n) = x
x = 2^n + 6
x - 6 = 2^n
2^n = x - 6
log 2^n = log (x-6)
n log 2 = log (x-6)
n = (x-6)/2
f^-1(x) = (x-6)/2
The range of years would be 493 to 745.
According to the empirical rule, 99.7% of data will fall within 3 standard deviations from the mean. Using this information, we have
619+3(42) and 619-3(42)
619+126 and 619-126
745 and 493
The x-coordinate of the vertex of a parabola y = ax^2 + bx + c is x = -b / (2a).
Here, a = -3 and b = -10, so the x-coord of the vertex is x = 10 / (2*-3), or
x = 10 / (-6) = -5/3
and so the y-coordinate is y = -3(-5/3)^2 - 10(-5/3) = 25/3
The vertex of this parabola is (-5/3, 25/3). (answer)