option A
option A
option C
option B
option D
Step-by-step explanation:
Exponential growth function: f(t) = a(1 + r)^t
Exponential decay function: f(t) = a(1 - r)^t
a) y = (0.9)^t/2
when the number in the bracket of the exponential function is less than 1, it is a decay
0.9 < 1
1 - 0.9 = 0.1
We say, the function is an exponetial decay (option A)
b) y = (0.81)^t
The number in the bracket of the exponential function is less than 1, it is a decay
1- 0.81 = 0.09
0.81 < 1
We say, the function is an exponetial decay (option A)
c) y = (1.08)^(t +6)
y = (1 + 0.08)^(t +6)
1.08 > 1
Here, the number in the bracket is greater than 1. Hence, it is an exponential growth (option C)
d) y = (0.85)^t
The number in the bracket of the exponential function is less than 1, it is a decay.
1 - 0.85 = 0.15
0.85 = 1 - 0.15
Rewritting it: y = (1 - 0.15)^t
Where 0.15 = r.
The rate of decay of the function is 15% (option B)
e) y = (1/2)^t
The number in the bracket of the exponential function is less than 1, it is a decay.
1/2 < 1. Also, 1/2 = 0.5
1 - 0.5 = 0.5
Rewritting the function: y = (1 - 0.5)^t
where r = 0.5
The rate of decay of the function is 50% (option D)