exponential functions
Determine the value of f(3)for the following function
f(x)=x+6
f(3)=(3)+6=9
25^(1/2)
5
sin30
sin30=1/2
f(x)=x-2
f(3)=(3)-2=1=1
32^(1/5)
2
d=12sin(30t)+14
where t is the time past 5am, in hours.
Determine the maximum and minimum depths of the water in the harbour.
MAX=26 MIN=2
f(x)=6x-1
f(3)=6(3)-1=62=3
If the growth factor was 4, and initially there were 8 people that had known the rumour, which of the following equations would model this situation
N=8(4t)
What is the period of the function
12 hours
Determine the vertex and x-intercepts of the parabola f(x)=3x2+6x-1
The x-coordinate:
x=-b2a=-62(3)=-66= -1
The y-coordinate:
f(-1)=3(-1)2+6(-1)-1=3-6-1= -4
Therefore the vertex is (-1,-4)
X-Intercepts
x=-bb2-4ac2a=-(6)62-4(3)(-1)2(3)=-636+126
-6+486=0.15or -6-486= -2.15
Therefore the two roots are 0.15 and -2.15
Bacteria A has an initial population of 500 and doubles every day, while bacteria B has an initial population of 50 and triples every day.
Write an equation for the population of each bacteria
N=500(2)
N=50(3)
How many hours during the day is the depth of the water above 14 metres
the depth of the water is above 14 metres for 12 hours every day
The height, h, in metres, above the ground of a football t seconds after it is thrown can be modelled by the function
h(t)=-4.9t2+19.6t+2
t=-b2a=-(19.6)2(-4.9)=19.69.8=2
After 10 days, which bacteria population is greater?
Bacteria B = N=50(3)
cos50
cos50=0.64