Solving Exponential Equations
Solve for x.
4^(3x)=sqrt4
x = 1/6
log_3(log_2(x))=0
x=2
The temperature of a bowl of soup, in degrees Fahrenheit, is
68+60e^(-kt)
where is the time since it was served, measured in minutes.
Determine the temperature of the soup when it was served.
128 degrees
There has been an outbreak of a certain virus in Maryland. The number of infected individuals is currently 15 and increases by 60% every 3 days.
Write a function that gives the number of infected individuals after t days.
y=15(1.6)^(t/3)
Solve for x.
2^(2x)⋅4^(3x)=√2
x=1/16
log_2(log_4(x))=1
x=16
The temperature of a bowl of soup, in degrees Fahrenheit, is
72+58e^(-kt)
where is the time since it was served, measured in minutes.
Determine the temperature of the soup when it was served.
130 degrees
There has been an outbreak of a certain virus in Maryland. The number of infected individuals is currently 15 and increases by 60% every 3 days.
How long will it take for the number of infected individuals to exceed 300?
x=19.122
about 19 days
3^x⋅9^(3x)=√3
x=1/14
Solve for x. Check for extraneous solutions.
log(x-1)+log(x+2)=1
x = 3
x = -4 (extraneous)
The temperature of a bowl of soup, in degrees Fahrenheit, is
68+60e^(-kt)
where is the time since it was served, measured in minutes.
If the soup is 100 degrees after 8 minutes, find the value of k.
k=0.079
There has been an outbreak of a certain virus in Maryland. The number of infected individuals is currently 100 and increases by 30% every 5 days.
Write a function that gives the number of infected individuals after t days.
y=100(1.3)^(t/5)
Solve for x.
3^(2x)+5*3^x-6=0
x=0
Solve for x. Check for extraneous solutions.
log_2(x+3)+log_2(x+2)=1
x = -1
x = -4 (extraneous)
The temperature of a bowl of soup, in degrees Fahrenheit, is
72+58e^(-kt)
where is the time since it was served, measured in minutes.
If the soup is 90 degrees after 7 minutes, find the value of k.
k= 0.167
There has been an outbreak of a certain virus in Maryland. The number of infected individuals is currently 100 and increases by 30% every 5 days.
On which day will the number of infected individuals exceed 500?
x=30.672
Solve for x.
2^(2x)+4*2^x-5=0
x=0
Solve for x. Check for extraneous solutions.
log_8(x+5)+log_8(x-2)=1
x = 3
x = -6 (extraneous)
The temperature of a bowl of soup, in degrees Fahrenheit, is
72+58e^(-kt)
where is the time since it was served, measured in minutes.
As time tends to infinity, the temperature of the soup approaches the temperature of the room. Determine the temperature of the room.
72 degrees
There has been an outbreak of a certain virus in Maryland. The number of infected individuals is currently 100 and increases by 30% every 5 days.
Does the model result in a reasonable answer when t=300?
y= 686,437,717
No, that is more than the whole population of Maryland.