Unit 4
Growth by constant ratio, and the inverse that recovers the exponent. Most of the unit follows from those two sentences.
Lesson 4.1
An exponential model multiplies by a constant factor over equal input intervals. The initial value is the output at input zero. A growth factor above 1 increases values, while a factor between 0 and 1 models decay. Identify the time unit before interpreting a percentage rate.
Lesson 4.2
A logarithm gives an exponent. Product and quotient rules require positive arguments over the real numbers. Apply the rules to factors, not terms of a sum. The power rule moves an exponent outside a logarithm when the relevant real-domain conditions hold.
Lesson 4.3
Use inverse operations to solve exponential and logarithmic equations. A logarithmic equation over the reals requires every original logarithm argument to be positive. Solving a transformed equation can produce candidates outside that domain, so check the original expressions.
Work through questions with a tutor and get help with the steps you find difficult.
Get help with this topic