Topic 5 Review

Front

Is the function linear or exponential?

Back

Exponential functions have a constant ratio of change, while linear functions have a constant difference. An exponential function can be identified by its form: y = a(b^x), where b > 1 for growth and 0 < b < 1 for decay.

Front

What type of function do the following points represent? {(-1,2),(0,10),(1,50),(2,250),(3,1250)}

Back

These points represent an exponential function because the ratio of y-values increases as x increases.

Front

Which function shows an initial amount of $15,000 and a decrease of 12% each year?

Back

The function is y = 15000(0.88)^x, where 0.88 represents a 12% decrease.

Front

Determine the y-intercept of the function y=3^x.

Back

The y-intercept is (0,1) because when x=0, y=3^0=1.

Front

Is the function f(x) = 300(1.16)^x growth, decay, linear or none?

Back

This function represents Exponential Growth because the base (1.16) is greater than 1.

Front

Define 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.

Front

What is the general form of a linear function?

Back

The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How can you identify exponential growth?

Back

Exponential growth can be identified by a base greater than 1 in the function f(x) = a(b^x). The y-values increase rapidly as x increases.

Front

How can you identify exponential decay?

Back

Exponential decay can be identified by a base between 0 and 1 in the function f(x) = a(b^x). The y-values decrease rapidly as x increases.

Front

What is the y-intercept of an exponential function of the form y = a(b^x)?

Back

The y-intercept is the point (0, a) because when x=0, y=a(b^0)=a.