Exponential functions

Practice 5 items →

f(x) = a·bˣ with growth for b > 1 and decay for 0 < b < 1, asymptote y = 0. Students evaluate and graph, read a as the start and b as the factor in a story, and write compound-interest and half-life models.

Specification · for a parent or teacher

Part no.: exponential-growth-decay
Course: High School Math 1 · Unit 10
Realm: Change
Difficulty: 4 of 4 — Grade 7 / Math 1 core. Structure, models, proofs on the grid.
Qty: 5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

evaluate and graph $a\cdot b^x$ ; classify growth vs decay from $b$ ; read $a$ as the starting value and $b$ as the growth factor in a story; write a compound-interest or half-life model.

Ready when

they can say whether $f(x)=800(0.5)^x$ is decay, give $f(0)$ and $f(3)$ , and name the half-life story.

Formulas

Exponential model

f(x) = a \cdot b^x

Compound interest

A = P\left(1 + \frac{r}{n}\right)^{nt}

Watch for

$2^{x+1}$ graphed as a shift of $2^x$ to the right; linear “add 2 each time” called exponential.

Before · requires

Exponentslaws-of-exponents · Math 1
Relations and functionsfunction-foundations · Math 1
Percentage: reverse percent and simple interestpercent-simple-interest · Math 7

After · used by

Comparing functionscomparing-function-families · Math 1

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