Exponents & Logarithms
3^4 * 3^10
What is
3^14 = 4,782,969
This is the "special logarithm" when converting e^x to logarithmic form.
What is the natural logarithm
ln(x)?
The growth of bacteria in a dish is modeled by the function f(t)=2^(t/3). When f(t) = 32, this is the value of t.
What is 15?
The equation V(t)=12000(0.75)^t represents the value of a motorcycle t years after it was purchased. This number represents the cost of the motorcycle when purchased.
What is $12,000?
This imaginary line is what an exponential and logarithm function has that "blocks" the graph from moving past a certain number.
What is an asymptote?
log_5(25)
without a calculator.
What is 2?
ln(e)
What is 1?
A house purchased 5 years ago for $100,000 was just sold for $135,000. Assuming exponential growth, the approximate the annual growth rate, to the nearest percent, is this number.
What is approximately 6%?
A=21000(1-0.12)^t is a model of exponential growth or exponential decay and the rate (percent) of change per time period is this number.
What is exponential decay and 12%?
This is the relationship between exponentials and logarithms.
What is they are inverses of each other?
This is what you do when two powers a multiplying with the same exponent but different bases.
What is multiply the bases and keep the exponent the same?
16^m=75
m is equal to this value (rounded to the nearest hundredth).
What is 1.56?
Newton's Law of Cooling is given by the function, T(t)=T_r+(T_i-T_r)e^(kt), where T(t) is the temperature of a heated substance t minutes after it has been removed from a heat (or cooling) source. T_i is the substance's initial temperature, k is a constant for that substance, and T_r is room temperature.
The initial temperature of a roast beef is 240^o , room temperature is 70^o , and k=-0.041 . This time is how long it will take to cool within one degree of room temperature.
What is 125 minutes?
The function A=220(1/2)^(t/12) can be used to model a situation, where A is the amount of pain reliever in milligrams remaining in the body after t hours. This function is a representation of this type of problem.
What is Half-Life?
An exponential function with a base of e is translated to the left 7 units and up 12 units. This equation can be represented like this.
What is
y=e^(x+7)+12?
The logarithm is equal to this equation:
7^x=43
What is
log_7(43)=x?
This is the value of x, to the nearest hundredth, in the equation 5^(x-8)-1=38.
What is 10.28?
This is, to the nearest tenth of a year, how long it would take an investment to double at a 3.75% interest rate, compounded continuously.
What is approximately 18.5 years?
The number of carbon atoms in a fossil is given by the function y=5100(0.95)^x , where x represents the number of years since being discovered. The percent of change each year is represented by this number.
What is 5%?
The x-intercept, rounded to the nearest hundredth, of the equation y=log_4(6x)-2 is this and is located at this point on a set of axes.
What is (170.67,0) that is located on the x-axis?
The simplified expression of ((4x^6)^2*(2x^7)^-3)/((6x^2)*(7x^2)^4) looks like this.
128/(14406x)
This is the value of p, to the nearest ten-thousandth, in the equation -8e^(10p-7)+5.1=-16.9
What is 0.8012?
The half-life of a radioactive substance is 15 years. Write an equation that can be used to determine the amount, s(t), of 200 grams of this substance that remains after t years. The time, to the nearest year, it will take for 1/10 of this substance to remain is this number.
What is approximately 50 years?
An equation to represent the value of a car after t
months of ownership is v=32000(0.81)^(t/12). This equation is an example of this type of problem.
What is exponential decay?
These are all the specific descriptions of the graph of y=log_3(x-4)-4.
What is
The asymptote is at x=4,
There is a horizontal shift 4 units to the right,
There is a vertical shift 4 units down,
The x-intercept is at (85,0),
A y-intercept does not exist?