Exponential Functions Test

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 a positive real number, and 'x' is the exponent. It represents growth or decay depending on the value of 'b.'

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' in the function f(x) = a * b^x is greater than 1, leading to an increase in value as 'x' increases. Exponential decay occurs when 'b' is between 0 and 1, resulting in a decrease in value as 'x' increases.

Front

Identify the type of function: f(x) = 2(1/7)^x.

Back

Exponential Decay.

Front

Identify the type of function: y = 7(5/4)^x.

Back

Exponential Growth.

Front

What is the formula for compound interest?

Back

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

Front

Calculate the amount in the account after 4 years if $2,200 is invested at 5.2% interest compounded daily.

Back

$2708.63.

Front

What does it mean if a function is increasing?

Back

A function is increasing if, as the input (x) increases, the output (f(x)) also increases.

Front

What does it mean if a function is decreasing?

Back

A function is decreasing if, as the input (x) increases, the output (f(x)) decreases.

Front

Given f(x) = 1.07^x, is this a growth or decay function?

Back

Growth.

Front

What is the base of an exponential function?

Back

The base of an exponential function is the constant 'b' in the function f(x) = a * b^x, which determines the rate of growth or decay.