Intermediate Algebra
Exponentials and Logarithms
Watch quantities grow and shrink by a constant factor: build exponential functions from tables and graphs, compare them with linear and quadratic growth, model interest and depreciation, shift them, and read them between whole numbers.
THE SYLLABUS
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Growing
When a number doubles again and again, each day is the day before times 2, so after n days a start of 5 has become 5 times 2 to the n: exponential growth.
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Doubling
Start from one and double every night: 1, 2, 4, 8, and after n nights 2 to the n. A function like f(n) = 2ⁿ, with the variable in the exponent, is an exponential function.
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Tripling
A quantity that triples each step goes 1, 3, 9, 27, and after n steps it is 3 to the n: g(n) = 3ⁿ. Tripling grows much faster than doubling, 2ⁿ.
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Powers of 10
Multiplying by 10 each step gives 1, 10, 100, 1,000: after n steps the count is 10 to the n, f(n) = 10ⁿ, and the exponent n counts the zeros.
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Level Check
Fifteen questions from Level 1: growth by 10, by 3 and by 2 written as expressions and evaluated, one count plotted, and growth read from patterns.
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