Exponential function

High school (ages 12+)
Mathematics & Numbers

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Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/exponential-function

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the inverse relationship?Exponential functions are the inverse of logarithmic functions
2. Why do exponential functions grow so fast?Because each step multiplies the current value by the base b, so the amount keeps getting bigger (or smaller) quickly. The rate of change is always proportional to the current value.
3. How does an exponential function look on a graph?It starts low and then shoots up quickly if b > 1, or slowly falls toward zero if 0 < b < 1. The curve gets steeper as x grows.

Transcendental Number: A number that is not a root of any non-zero polynomial equation with integer coefficients.
Derivative: The instantaneous rate of change of a function with respect to one of its variables.
Geometric Progression: A sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number.