enVision Topic 6 review

Front

What is the function that models the decrease of a bacterial colony by 14.9% per minute?

Back

f(x) = 12000(1 - 0.149)^{x}

Front

What type of formula is represented by f(x) = a_1 * r^{(n-1)}?

Back

Explicit formula

Front

What is the exponential function for a savings account that starts with $400 and gains 3% every year?

Back

f(x) = 400(1 + 0.03)^{x}

Front

Is the function f(x) = 2(1.25)^{x} an example of growth or decay?

Back

Exponential Growth

Front

What does an exponential growth function look like?

Back

It increases rapidly as x increases.

Front

What does an exponential decay function look like?

Back

It decreases rapidly as x increases.

Front

What is the general form of an exponential growth function?

Back

f(x) = a(1 + r)^{x} where r > 0.

Front

What is the general form of an exponential decay function?

Back

f(x) = a(1 - r)^{x} where r > 0.

Front

If a population of bacteria decreases by 20% per hour, what is the decay factor?

Back

0.80 (since 1 - 0.20 = 0.80)

Front

What is the difference between an explicit formula and a recursive formula?

Back

An explicit formula gives the nth term directly, while a recursive formula defines each term based on previous terms.