Unit 5, Flashcard 1 Review

Front

What type of function is f(x)=2(1/7)^{x} ?

Back

Exponential Decay

Front

What is the Growth/Decay factor of the function f(x)= 2(4)^{x} ?

Back

4

Front

Write an explicit rule for the geometric sequence 5, 15, 45, ...

Back

a_n = 5(3)^{n-1}

Front

Find a_{12} for the geometric sequence defined by a_n = 6(2)^{n-1}

Back

12,288

Front

Find the common ratio for the geometric sequence: 10, 20, 40, 80

Back

2

Front

Define an exponential function.

Back

A function of the form f(x) = a(b)^{x}, where a is a constant, b is the base, and x is the exponent.

Front

What is the formula for the nth term of a geometric sequence?

Back

a_n = a_1 * r^{n-1}, where a_1 is the first term and r is the common ratio.

Front

How do you determine the common ratio in a geometric sequence?

Back

Divide any term by the previous term: r = a_n / a_{n-1}.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base of the exponent is greater than 1, while exponential decay occurs when the base is between 0 and 1.

Front

What is the explicit formula for the geometric sequence 3, 6, 12, ...?

Back

a_n = 3(2)^{n-1}