A function that contains a variable in the exponent
100
Convert the following to Logarithmic Form:
3^3 = 27
log base 3 (27) = 3
100
Write each in exponential form:
log base 4 (625) = 4
5^4 = 625
100
In 1981, the whale population was 350 and has increased at a rate of 14% each year. Write and exponential function and predict when the population will reach 20,000.
a. A(t) = 350(1+0.14)^t
b. 31 years or 2012
100
evaluate the following function for f(3):
f(x) = -4x+10
f(3) = -2
200
Growth or Decay?
f(x) = 32(0.5^x)
Exponential Decay
200
Evaluate:
log base 7 (343)
3
200
Write in exponential form:
log base 4.5 (1) = 0
4.5 ^ 0 = 1
200
A scooter purchased for $10,000 depreciated at 15% each year. Write and exponential equation and predict when the value will fall below $100
a. A(t) = 10,000(1-0.15)^t
b 29 years
200
Simplify the expression (non decimal answer):
sqrt(20)/sqrt(120)
sqrt(6)/6
300
Growth or Decay?
f(x) = 4(3/4)^x
Exponential Decay
300
Evaluate the following using mental math:
log base 0.1 (100)
-2
300
Solve the following:
5 ^ x = 50
x = 2.43
300
In 2000 the population of the world was 6.1 billion. If it continues to increase at 1.4% what would the population be in 2020? When does the population surpass 10 billion?
a. 8.06 billion
b. 2036
300
Express each number in terms of i:
5 sqrt (-48)
20i sqrt(3)
400
Growth or decay?
g(x) = 500(1+0.14)^x
Exponential Growth
400
Solve the following:
log (5x) - log (15.5) = 2
x = 310
400
Solve the following:
3 ^ (x-1) = 1/9
x = -1
400
How many years would it take for an initial investment of $100 increasing at a rate of 4% quarterly to reach $200
4.5 years
400
determine where (x+2) is a factor of:
3x^3 + 11x^2 +2x - 16 algebraically
Yes it is!
500
Graph the following exponential equation using a table:
f(x) = .5(2^x)
??????
500
Solve:
log(x) - log(x/100) = x
x = 2
500
Solve the following:
13 ^ (3x-1) = 91
x = 0.92
500
A new softball dropped from a height of 25 inches rebounds to about 2/5 the height on each successive bounce. After how many bounces would a softball bounce less than 1 inch