Parts of an Exponential Equation

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

Mathematical Equivalence

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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.

Consider the equation y = 4(1.67)^x where y is the area covered by mutant venus fly trap plants and x is the number of years since they were discovered. Which of the following statements is true?

• If x = 0, there are 4 square kilometers of island covered by mutant venus fly traps.

• If x = 0, all the mutant venus fly trap plants have been killed by an herbicide.

• If x = 0, the x-intercept of the graph of the scenario is (0 , 0)

• If x = 0, there are 1.67 square kilometers covered by mutant venus fly trap plants.

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

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. How many years will it take for the plants to occupy 400 km²?

• 8 years

• 9 years

• 10 years

• 11 years

This graph models y = (0.2)^x - 3. Which statement describes what happens to the y value as x increases?

• As the value of x becomes very large, the value of y approaches - 0.2.

• As the value of x becomes very large, the value of y approaches -3.

• As the value of x becomes very large, the value of y approaches -2.

• As the value of x becomes very large, the value of y will gradually

  decrease to negative infinity.