Half-Life. We now turn to exponential decay. One of the common terms associated with exponential decay, as stated above, is half-life, the length of time it takes an exponentially decaying quantity to decrease to half its original amount.

For example, the half-life of strontium-90 is 28.8 years. If you start with 10 grams of 90Sr and wait 28.8 years, you’ll have 5 grams left of 90Sr. If another 28.8 years go by, 2.5 grams will remain.

29 years

1. Radioactive decay shows disappearance of a constant fraction of. activity per unit time.
2. Half-life: time required to decay a sample to 50% of its initial. activity: 1/2 = e –(λ*T1/2)
3. Constant in time, characteristic for each nuclide. Convenient to calculate the decay factor in multiples of T1/2:

What is a drug’s half-life? The half-life of a drug is the time it takes for the amount of a drug’s active substance in your body to reduce by half. This depends on how the body processes and gets rid of the drug.

How to Calculate a Decay Factor

1. “y” is the final amount remaining after the decay over a period of time.
2. “a” is the original amount.
3. “x” represents time.
4. The decay factor is (1–b).
5. The variable, b, is the percent change in decimal form.

exponential growth or decay function is a function that grows or shrinks at a constant percent growth rate. The equation can be written in the form f(x) = a(1 + r)x or f(x) = abx where b = 1 + r.

As you can see from this table, the amount of reactant left after n half-lives of a first-order reaction is (1/2)n times the initial concentration….Half-Lives and Radioactive Decay Kinetics.

In mathematics, exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula y=a(1-b)x wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed.

Because exponential growth indicates constant growth rate, it is frequently assumed that exponentially growing cells are at a steady-state. However, cells can grow exponentially at a constant rate while remodeling their metabolism and gene expression.

To find the average rate of change, we divide the change in the output value by the change in the input value.

The slope is the average rate of change about a point as the interval over which the average is being taken is reduced to zero. the slope of f(x) at x is indicated by the blue line.

A rate of change relates a change in an output quantity to a change in an input quantity. The average rate of change is determined using only the beginning and ending data. See (Figure). Identifying points that mark the interval on a graph can be used to find the average rate of change.

Since the average rate of change of a function is the slope of the associated line we have already done the work in the last problem. That is, the average rate of change of from 3 to 0 is 1. That is, over the interval [0,3], for every 1 unit change in x, there is a 1 unit change in the value of the function.

1 Answer. The average rate of change gives the slope of a secant line, but the instantaneous rate of change (the derivative) gives the slope of a tangent line. Also note that the average rate of change approximates the instantaneous rate of change over very short intervals.

1 Answer. The average rate of change is constant for a linear function. Another way to state this is that the average rate of change remains the same for the entire domain of a linear function. If the linear function is y=7x+12 then the average rate of change is 7 over any interval selected.

Limits are the link between average rate of change and instantaneous rate of change: they allow us to move from the rate of change over an interval to the rate of change at a single point.

A constant rate of change means that something changes by the same amount during equal intervals. A graph that has a constant rate of change is a line, and the rate of change is the same as the slope of the line.

Students interpret slope as rate of change and relate slope to the steepness of a line and the sign of the slope, indicating that a linear function is increasing if the slope is positive and decreasing if the slope is negative.

Using the Slope Equation

1. Pick two points on the line and determine their coordinates.
2. Determine the difference in y-coordinates of these two points (rise).
3. Determine the difference in x-coordinates for these two points (run).
4. Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0). because division by zero is an undefined operation.

Slope is a measure of steepness. Some real life examples of slope include: in building roads one must figure out how steep the road will be. skiers/snowboarders need to consider the slopes of hills in order to judge the dangers, speeds, etc.

Zero (Horizontal) Slope The sunset on the horizon is an example of a zero slope because it goes horizontally. This picture represents a zero slopebecause it’s a bridge goinghorizontally.

Slopes come in 4 different types: negative, positive, zero, and undefined. as x increases.

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as “rise over run” (change in y divided by change in x).

y intercept