16] The table represents and exponential growth, this is because as the domain values increase, the range values also increase. This means that the resulting curve will be an exponential growth curve.
17] The table represents an exponential decay curve. It can be seen that the values of the range are decreasing at a constant rate as the values of the domain increases. The resultant curve will be an exponential decay curve.
18] 2,4,6,8,....
The sequence is an arithmetic sequence, the common difference of the sequence is 2.
19] 5,-10,20,-40,...
The sequence is a geometric sequence, this is because it has a common ratio of (-10/5)=-2.
20] 4,9,16, 25,...
The sequence is neither arithmetic nor geometric sequence. This is because it does not have a common difference or a common ratio.
21] -64,-32,-16,-8,....
The sequence is geometric sequence. This is because it has a common ratio which is given by -64/-32=2.
22. The recursive formula for the sequence 25,10, -5 will be:
common difference=15
hence the recursive formula will be:
an=a_(n-1)-15
23. The recursive formula for the sequence given by -10,-6,-2,2 will be:
common difference=4
thus the recursive formula will be:
an=a_(n-1)+4
24] a1=4, a2=-2
when the sequence is arithmetic:
common difference will be:
a2-a1=-2-4=-6
the third term will be:
an=a+(n-1)d
an=4+(3-1)(-6)
an=4-12
an=-8
when sequence is geometric:
common ratio=-2/4=-1/2
the third term will be:
a3=4(-1/2)^(3-1)
a3=4(-1/2)^2
a3=1
hence:
a3+b3=-8+1=-7
Answer: -7
25. y=2^x; x=5
evaluating this we get:
y=2^5=32
Answer: 32
26] f(x)=3(4)^x; x=-1
evaluating this we get:
f(-1)=3(4)^(-1)
f(-1)=3/4=0.75
Answer: 0.75
27] f(x)=1/2(5)^x; x=3
evaluating this we get:
f(3)=1/2(5)^3
f(3)=62.5
Answer: 62.5
28] y=0.5^x; x=-4
Evaluating the above we get:
y=0.5^(-4)
y=1/0.5^4
y=1/16
29] Given that the bacteria doubles every minute, the y-values for the table will be as follows:
x=0,1,2,3,4,5,6
y=0,2,4,6,8,10,12
