Back to Compare exponential and polynomial growth — Problem 2 · Task Set 58

Exercises: Compare Exponential and Polynomial Growth

Work through each section in order. Show your work where indicated.

Grade 9·21 problems·~30 min·Common Core Math - HS Functions·group·hsf-le-a-3

Work through problems with immediate feedback

Fluency Practice

Values of $f(x) = 500x$ and $g(x) = 1.5^x$ at selected points: at $x = 20$ , $f = 10{,}000$ and $g = 3{,}325$ ; at $x = 25$ , $f = 12{,}500$ and $g = 25{,}251$ ; at $x = 30$ , $f = 15{,}000$ and $g = 191{,}751$ .

Which statement is correct?

The linear function will always be larger because it has a bigger coefficient (500 vs 1.5).

The crossover occurs between $x = 20$ and $x = 25$ , after which the exponential dominates.

The exponential is always larger because $1.5^{25} > 500 \times 25$ .

Neither function dominates — they oscillate in which is larger.