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September 17, 2019September 26, 2019

Linear versus Exponential Growth and Decay

Calculus 1, Lectures 3A and 3B

For $f(x)=2\cdot 1.5^{x}$ , $f(x+2)=1.5^{2}f(x)$ , no matter what $x$ is. The exponential function is converting addition of inputs to multiplication of outputs.

f(x)=2\cdot 1.5^{x} — For $f(x)=2\cdot 1.5^{x}$ , $f(x+2)=1.5^{2}f(x)$ , no matter what $x$ is. The exponential function is converting addition of inputs to multiplication of outputs.

Linear functions are constructed from the arithmetic building blocks of repeated addition and subtraction. In a similar manner, exponential functions are constructed from repeated multiplication and division.

These sentences describe both the most basic similarity … Read the rest