Topic 5 Review

Front

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

Back

The nth term of a geometric sequence can be expressed as: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

Find the first four terms of the sequence given the rule: a_n = 4(5)^(n-1)

Back

The first four terms are: 4, 20, 100, 500.

Front

What does the variable k represent in the equation y=2^x+k?

Back

The variable k represents a vertical shift of the graph of the function y=2^x. A positive k shifts the graph up, while a negative k shifts it down.

Front

If the population of mosquitoes grows at a rate of 25% per month, how do you calculate the population after a certain number of months?

Back

You can use the formula: P = P_0 * (1 + r)^t, where P_0 is the initial population, r is the growth rate (as a decimal), and t is the number of time periods (months).

Front

What is the common ratio in a geometric sequence?

Back

The common ratio (r) is the factor by which each term in the sequence is multiplied to get the next term.

Front

Find the common ratio for the sequence: 4, -16, 64, -256.

Back

The common ratio is r = -4.

Front

What does the graph of y=4^x-2 represent in relation to y=4^x?

Back

The graph of y=4^x-2 is the graph of y=4^x shifted down 2 units.

Front

How do you determine the value of k in the equation y=2^x+k if given a graph?

Back

You can determine k by observing the vertical shift of the graph compared to the parent function y=2^x.

Front

What is the formula to calculate the future value of an investment with compound interest?

Back

The formula is: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

What is exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time.