This is a free lesson from our course in Algebra II
This lesson explains how to solve the realworld exponential growth and decay problems. Exponential decay is generally applied to word problems that involve financial applications as well as those that deal with radioactive decay, medicine dosages, and population decline. To decay exponentially means that the topic being studied is decreasing in proportion to the amount that was previously present. This type of problem requires that you write an exponential decay function based on given information. You must then correctly substitute given values for variables and solve the equation you obtain. In solving the equation you must convert the exponential equation to a log equation and correctly use various properties of logarithms. At the conclusion of the problem, you should always check for the reasonableness of your solution.
(More text below video...)
(Continued from above)
In order to solve
such problems, remember to:
• know how to solve an exponential equation
• know the properties of logarithms
• know how to analyze and understand the problem
• write and solve an equation for the problem. Exponential functions are of the form y = a^{x}
+ b, where a is any real constant. It illustrates how to solve
the word problems for which the halflife is given using the formula
A = A_{0}e^{kt},
where A is the amount/quantity left after t years, A_{0} is the
initial amount, t is the number of years and k is the decay constant.
Simply to say, look at exponential function x^{3}, where 3 is the
base and x is the exponent and the latter is variable. The general exponential
function for x = 1.2, looks like: f(1.2) = 1.276 1.2. The formula developed
from defined functions application can be used to solve related word problems.
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