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TexasMaths

Exponential Functions and Equations

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you solve real-world exponential problems like population, depreciation, and compound interest, and read values from the model?

Solve real-world problems modeled by exponential functions, including population growth, depreciation, and compound interest, evaluate the model, and use technology to find an exponential best fit (TEKS A.9B, A.9E).
A STAAR Algebra I answer on real-world exponential problems (TEKS A.9B, A.9E) - population growth, depreciation, compound interest - evaluating the model at a value and finding an exponential best fit with technology.
10 min answer →

How do you write an exponential function in the form f(x) = ab^x, interpret a and b, and tell growth from decay?

Write exponential functions of the form $f(x) = ab^x$ to model growth and decay, interpret the meaning of $a$ and $b$ in context, and determine whether a situation represents exponential growth or decay (TEKS A.9B, A.9C, A.9D).
A STAAR Algebra I answer on exponential functions f(x) = ab^x (TEKS A.9B, A.9C, A.9D), interpreting the initial value a and base b, and distinguishing growth (b greater than 1) from decay (b between 0 and 1).
10 min answer →

How do you graph an exponential function and identify its key features: the y-intercept, the asymptote, and growth or decay?

Graph exponential functions that model growth and decay and identify key features, including the y-intercept and the asymptote, and determine the domain and range (TEKS A.3C, A.9A, A.9F).
A STAAR Algebra I answer on graphing exponential functions and reading key features (TEKS A.3C, A.9A, A.9F) - the y-intercept, the horizontal asymptote, growth versus decay shape - and the domain and range.
10 min answer →

How do you solve a simple exponential equation by rewriting with a common base, and how do you distinguish linear from exponential situations?

Solve exponential equations using the properties of exponents (rewriting with a common base), and distinguish between situations that can be modeled with linear functions and with exponential functions (TEKS A.9D, A.9G).
A STAAR Algebra I answer on solving simple exponential equations by common base (TEKS A.9D) and distinguishing linear from exponential growth (TEKS A.9G) - constant difference versus constant ratio.
9 min answer →