Exponential Functions and Models

Flashcards covering exponential growth and decay formulas, interest calculations, and radioactive decay based on lecture notes.

The standard formula for exponential growth is __________.

$$f(t) = A(1+r)^t$$

The standard formula for exponential decay is __________.

$$f(t) = A(1-r)^t$$

If a deer population in 2000 was $1100$ and decreases at a rate of $4\%$, the expression to find the population after $5$ years is __________.

$$1100(1-0.04)^5$$

If Joe borrows $500$ at $8\%$ interest, the equation representing the amount owed $f(t)$ after $t$ years is __________.

$$f(t) = 500(1+0.08)^t$$

If Mary invests $2000$ at $0.6\%$ interest compounded annually, the equation for the amount in her account $f(t)$ after $t$ years is __________.

$$f(t) = 2000(1+0.006)^t$$

A radioactive element decays according to the equation $y = A(\frac{1}{2})^{\frac{t}{200}}$; if $9000\text{ grams}$ were present initially, the amount remaining after $400\text{ years}$ is __________.

$$2250\text{ grams}$$

In a table where time $x$ increases by $1$ and population $y$ doubles from an initial value of $5$ ($5, 10, 20, 40...$), the correct modeling equation is __________.

$$y = 5(2)^x$$