中4maths

17. y = (1/6)^x = [6 ^(-1)]^x = 6^(-x).
Based on the principle y = f(-x) is a reflection of y = f(x) about the y - axis, so the 2 curves are symmetrical. The axis of symmetry is x = 0.
18.
y = log x to the base 1/7 = log x to the base 7/log (1/7) to the base 7 [Change of base].
= log x (base 7)/log (7 ^ -1) (base 7)
= log x (base 7)/-1 log 7 (base 7)
= log x (base 7)/ -1.
= - log x (base 7).
Based on the principle y = - f(x) is a reflection of y = f(x) about the x - axis, the 2 curves are symmetrical. Axis of symmetry is y = 0.
19. P = 1040 (1.0001)^ -x
When x = 0 (that is on the ground), P = 1040 (1.0001)^0 = 1040.
When x = 3000, P = 1040(1.0001)^ -3000 = 1040/1.3498 = 770.5