**rate = k m n p** … in which , , and represent the molar concentrations of reactants, and k is the rate constant, which is specific for a particular reaction at a particular temperature.

The activity of a sample is directly proportional to the number of atoms of the radioactive isotope in the sample: A=kN. Here, the symbol k is the **radioactive decay constant**, which has units of inverse time (e.g., s ^{−}^{1}, yr ^{−}^{1}) and a characteristic value for each radioactive isotope.

**Simple Interest Formulas and Calculations:**

- Calculate Interest, solve for I. I = Prt.
- Calculate Principal Amount, solve for P. P = I / rt.
- Calculate rate of interest in decimal, solve for r. r = I / Pt.
- Calculate rate of interest in percent. R = r * 100.
- Calculate time, solve for t. t = I / Pr.

The specific rate constant (k) is **the proportionality constant relating the rate of the reaction to the concentrations of reactants**. The rate law and the specific rate constant for any chemical reaction must be determined experimentally. The value of the rate constant is temperature dependent.

Because this equation has the form y = mx + b, a plot of the natural log of as a function of time yields a straight line. The rate constant for the reaction can be determined **from the slope of the line**, which is equal to -k.

The integrated rate law for the zero-order reaction A → products is _t = -kt + _0. Because this equation has the form y = mx + b, a plot of the concentration of A as a function of time yields a straight line. **The rate constant for the reaction can be determined from the slope of the line, which is equal to -k**.

The answer is: **k=2** . Given two point, A(xa,ya) and B(xb,yb) the slope of the line that passes from them is: m=yb−yaxb−xa .

'k' is the **rate constant** of the first-order reaction, whose units are s^{-}^{1}. '' denotes the concentration of the first-order reactant 'A'. d/dt denotes the change in the concentration of the first-order reactant 'A' in the time interval 'dt'.

Question: What is the half-life for the first-order decay of carbon-14? The rate constant for the decay is **1.217×10−4year−1** 1.217 × 10 − 4 y e a r − 1 .

**rate = k m n p** … in which , , and represent the molar concentrations of reactants, and k is the rate constant, which is specific for a particular reaction at a particular temperature.

The units of the rate constant, k, depend on the overall reaction order. The units of k for a zero-order reaction are M/s, the units of k for a first-order reaction are 1/s, and the units of k for a second-order reaction are **1/(M·s)**.

Introduction. Questions relating to machine input-output or simply input-output are **a series of statements in different steps and is stated in jumbled manner**. It is a kind of computer or word-processing machine and this machine performs some operations on the input that is given.

Work input is defined as **the effort force multiplied by the distance across which the force is exerted to a machine**. Work output is defined as the resistance force multiplied by the distance over which the force is applied. The work output of an ideal machine is equal to the work input, i.e. efficiency.

The input is sometimes called the **independent variable**. Functions are often expressed in function notation. In function notation, the equation used earlier as an example of a function, y = x + 5 y = x + 5 , would be expressed as f(x) = x + 5 f ( x ) = x + 5 . In this example, x is the input.

In mathematics, a function is any expression that produces exactly one answer for any given number that you give it. The input is **the number you feed into the expression**, and the output is what you get after the look-up work or calculations are finished.

Dated : 08-Jul-2022

Category : Education