Revisit Exponential Function and Geometric Sequences

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a(b^x), where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

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

Back

The common ratio (r) can be found by dividing any term by the previous term: r = a_n / a_(n-1).

Front

What is the common ratio for the sequence: 28, 14, 7, 3.5...?

Back

The common ratio is 1/2.

Front

What is the common ratio for the sequence: 64, -16, 4, -1...?

Back

The common ratio is -1/4.

Front

Is the sequence 2, 4, 8, 16... a geometric sequence?

Back

Yes, it is a geometric sequence.

Front

What does 'a' represent in the function f(x) = 300(1.16)^x?

Back

In this function, 'a' represents the starting term, which is 300.

Front

Which function shows an initial amount of $15 and an increase of 35% each year?

Back

The function is y = 15(1.35)^x.

Front

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

Back

The nth term can be calculated using the formula a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

What is the value of the first term in the sequence 5, 10, 20, 40...?

Back

The first term (a_1) is 5.