The Exponential Function and Its Applications

Pure Mathematics — Second Secondary

Common mistakes

Comparison aspect	Main idea	Keywords
Confusing an exponential function with a power function	2^x is exponential, while x² is a quadratic function.	whilequadratic
Using a percentage as a whole number	5% is written as 0.05 not 5	written
Forgetting the 1 in compound growth	the factor is (1 + r) not r	factor
Confusing growth with decay	if the base is less than 1 the function decreases even when the exponent is positive	baselessfunctiondecreases
Treating half-life as subtraction	the quantity is not reduced by a fixed amount but is halved after each period	quantityreducedfixedamount

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