Parts of Exponential Equations
Is the following growth or decay: f(x) = 2x
Growth
Write an exponential function whose graph passes through (0,-2) and (3,-16)
y = -2(2)x
State the domain and range
y = 4(2)x
Range: y > 0
Expand:
log47p2q
log47+2log4p+log4q
Evaluate:
log82
1/3
Is the following growth or decay: f(x)=100*(0.5)x
Decay
Write the equation of an exponential function which passes through points (0, 9) and (2, 1)
y = 9(1/3)x
What is the horizontal Asymptote?
y = 7(5)x
y = 0
Write as one logarithm:
(1/2)(log23+log25)
log2(15)1/2
Evalutate:
log9(3)1/2
1/4
Use y = 250(1.2)t What is the growth rate?
20%
Write the equation of an exponential function which passes through the points (0, 10) and (1/2, 10/3)
f(x) = 10(1/9)x
What is the y-intercept?
y = 2(1/9)x
(0, 2)
Expand:
log5x4y
4log5x+log5y
Solve for x:
log4(3x-5) = log410
x = 5
Is the following growth or decay: f(x) = 7 (0.94)x
Decay
The fish in The Magic Forest Lake were declining at an annual rate at 1.5%. Their current number is estimated at 2500. Write an equation to model the decreasing number of fish.
y = 2500(.985)x
State domain, range, y-intercept, and horizontal asymptote
y = -5(1/3)x
Domain: all real numbers
Range: y < 0
y-intercept: (0, -5)
horizontal asymptote: y = 0
Write as one logarithm:
log56-2log5y-log52m
log5(3/y2m)
Solve for x:
log3(x+2)+log36=3
x = 5/2
y = 9.8(1.35)t What is the growth rate?
35%
The squid in The Magic Forest Lake were declining at an annual rate at 5.5%. Their current number is estimated at 50,000. Write an equation to predict the number of squid in the lake in 10 years.
f(10) = 50000(.945)10 and 28,398 squid
Graph
y = 2(3)x
Expand:
log10(m/n2)1/2
(1/2)log10m-log10n
Solve for x:
log3(2x+1)<2
(-1/2)<x<4