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HSF.LE.A.3 Tutor Intake — Exponential vs. Polynomial Growth

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Grade 9·10 problems·~14 min·Common Core Math - HS Functions·group·hsf-le-a-3

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For $f(x) = 1000x$ and $g(x) = 2^x$ , which of the following
best explains why the exponential eventually overtakes the linear
function?

The exponential adds a constant amount each step, and that
amount eventually exceeds 1000.

The exponential multiplies by 2 each step, so its increment
at each step equals its current value and grows exponentially,
while the linear function adds only 1000 each step.

The exponential grows by a fixed percentage that is larger
than the linear function's slope.

The coefficient 1000 shrinks over time, making the linear
function grow more slowly.