Answer:
The sign of the function is positive because it´s an exponential function so the graph will be above
the x-axis and there is no x-intercepts.
The y-intercept is (0,f(0))=(0,1/5)
Since the base (1/5) < 1 f(x) it´s a decreasing function,
Lim f(x) when x tends to ∞ = 0+
Lim f(x) when x tends to –∞ = +∞
(f°g)(x)=f(g(x))=f(√(x-3))=( √(x-3))2-6= x-3-6=x-9
(g°f)(x)=g(f(x))=g(x2-6)=√(x2-6-3)= √(x2-9)=
We must find t where A(t)=1037
993.9e0.006t=1037
e0.006t=1037/993.9=1.0433645
Ln(e0.006t)=Ln(1.0433645)
0.006t=0.0424506
t = 0.0424506/0.006=7.075
Rounding to the nearest integer t=7 (year 2010)
Answer: In the year 2010