Lesson 7.2: Exponential Functions

Question 1

Discrete

Answer 1

the sequence has values only at distinct points (the 1st term, 2nd term, etc.)

Question 2

Continuous

Answer 2

The function has values for all possible values of x. The integers are included, but also all the numbers in between.

Question 3

Exponential Function

Answer 3

y=a(b^x)+c or f(x)=a(b^x)+c a is the starting amount, and b is the amount by which the total is multiplied each time. Notice that the x value, the variable that is changing, is in the exponent spot. The constant c represents anything that is added or subtracted separately from the multiplication. (It works much like the c in quadratic functions.) For example, the bacteria problem from earlier would have the equation y=3000(2x).

Question 4

Asymptote

Answer 4

When c=# it is the boundary line of the function and never quite reaches the boundary exactly, but forever get’s closer.
The horizontal asymptote is y=c. (Some other types of functions have vertical asymptotes, but we will not address those in this course.)

Question 5

Exponential Growth

Answer 5

When we raise a number greater than 1 to the power of x, it gets bigger as x gets bigger.

Question 6

Exponential Decay

Answer 6

When we raise a number smaller than 1 to the power of x, it gets smaller as x gets bigger