Parts of the Exponential Equation

Identify the y-intercept (initial value) in the function f(x)=13(.27)^x

• (.27)^x
• .27
• 13
• 3.51

The amount of money in your bank account per month, x, is modeled by the equation y=1,000(1.12)^x. What is the initial value?

• 1,000

• 1.12

• .12

• 12%

Given the function y=5(0.6)^x what is the initial value?

• 5

• 0.6

• 500

• 60

What is it about the equation y = 2(9/7)^x that indicates that it is a model for exponential growth?

• The equation is growth because 2 is positive.

• The equation is growth because the factor is positive.

• The equation is growth because the factor is greater than one.

• The equation is growth because the exponent is always positive.

Consider the equation y=200(1.08)^x which models the increase in value of an autographed Annie program. Let y = the value of the item, let x = the number of years since the performance. What does the 1.08 in the equation indicate?

• The value of the item is increasing by $1.08 each year.

• The value of the item is increasing by 1.08% each year.

• The value of the item will increase to $200 1.08 years after purchase.

• The value of the item is increasing by 8% each year.

If you were asked to write an exponential function with an asymptote of y = - 2, what must you include in your equation?

• Subtract 2 from any exponential expression. Ex. y = (4)^x - 2

• Add 2 to any exponential expression. Ex. y = (4)^x + 2

• Raise the expression to the power of -2. Ex. y = x ^-2

• Subtract .02 from 1 to get a decay factor. Ex. y = (1 - .02)^x

A population of mutant venus fly trap plants are taking over an island in the South Pacific, capturing everything from insects to small rodents. When they were first discovered they covered 4 square kilometers. As the population grows, the plants spread and cover more land. Use the table to write an equation.

• y=4(4)^x

• y=4(2.68)^x

• y=4(1+1.67)^x

• y=4(1.67)^x

What parts of an exponential equation could you find in a table?

• The factor is found as the first difference in the table, and the value of a is where y=0.

• The factor is found as the common ratio in the table, and the value of a is where y = 0.

• The factor is found as the common ratio in the table, and the value of a is where y = 0.

• The factor is found as the first difference in the table, and the value of a is where x=0.

The diagram shows the function f(x) = 3^x + 2. How could you name an ordered pair of this function.

• Option 1: Plug the function into the calculator and look at the table.

• Option 2: Randomly write down your favorite numbers.

• Option 3: Plug in zero for x, which gives an y output of 3 (1+2) for the point (0, 3)

• Option 1 and 3

• None of the above

Consider the equation 70(0.8)^x + 2. What is the equation of the asymptote?

• y = 70

• y = 0.8

• y = 2

• y = 0.2