5.5 Comparing Linear and Exponential Growth

3 practice questionsNot yet reviewed

Notes

Linear functions grow by a constant amount; exponential functions grow by a constant factor.

Exponential growth eventually exceeds any linear function, even if it starts smaller.
To identify a table: constant differences mean linear; constant ratios mean exponential.
Example: $y = 4, 7, 10, 13$ has constant differences of 3, so it is linear.
To compare, evaluate both functions at several inputs.

For large values of $x$, which grows faster?

A table gives $y = 4, 7, 10, 13$ for $x = 0, 1, 2, 3$. What type of function is it?

Let $f(x) = 50 + 10x$ and $g(x) = 2^x$. For whole numbers $x$, what is the least $x$ where $g(x)$ is greater than $f(x)$?