Graphs
List the transformations:
f(x)=3*4^x-2
Dilation by 3, down 2
Simplify:
log1000
3
log_3(x-7)-2=2
x=88
What does half-life mean?
The time it takes for a substance to decay by half.
Rewrite as an exponent:
log_4 64=3
4^3=64
List the transformations:
g(x)=log(x-7)+5
right 7, up 5
Evaluate:
log_8 1=x
x=0
log(x-2)+log(x)=log(10x)
x=12
What is the formula for compound interest?
A=P(1+r/n)^(nt)
Rewrite as a log:
e^3=20.0855
ln3=20.0855
List the transformations:
y=-1/2e^x+8
reflection across x-axis, dilation by 1/2, and up 8
Condense as much as possible:
4log_2(x)-3log_2(y)
log_2(x^4/y^3)
e^(2x)-5e^x-14=0
x=ln7=1.9459
If you put $3000 into a savings account with 2% interest that is compounded quarterly, how long will it take for the account to grow to $4000?
14.42 years
Evaluate:
log_3 (1/27)=x
x=-3
List the transformations:
y=log(-(x+2))-6
reflection across y-axis, left 2, down 6
Condense as much as possible:
1/3ln(x+1)+1/4ln(y)
ln[(x+1)^(1/3)*y^(1/4)]
3+2^(4x)=12
x=0.7925
The half-life of radium-223 is 11.4 days. If there is 55 kBq/kg present, how long will it take to decay to 20 kBq/kg?
14.705 days
Expand as much as possible:
log_9(3/x^8)
1/2-8log_9x
Where is the following graph increasing and decreasing?
g(x)=-3^x+2
increasing: none decreasing: all real numbers
Expand as much as possible:
log((x^2y^7)/z^3)
2logx+7logy-3logz
3^(x+4)=7^(2x+3)
x=-0.5167
The half-life of caffeine is 5 hours. You need to have less than 30mg in your bloodstream to go to sleep. A venti pumpkin spice latte has 225mg of caffeine. If you want to go to bed by 10:00pm, what is the latest time you should start drinking the latte?
approximately 7:30 am
-2+3*e^(x+8)=13
x=-6.3906