Exponential Growth Functions from Tables

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

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

If you are given the following tables, how would you fill in the missing values?

• Find the common difference for the linear table and use that to find the other y values and for the exponential table find the first difference and use that to find the other y values.

• Use the second difference to find the linear table values and the third difference to find the exponential table values.

• Find the first difference for the linear table and use that to find the other y values and for the exponential table find the common ratio and use that to find the other y values.

• Give up.

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.

Does the table below represent exponential growth or decay?

• Exponential Growth

• Exponential Decay

Write the function for the following table:

• f(x) = 5x + .08

• f(x)= 5x + 2

• f(x) = .08(5)^x

• f(x)= 2(5)^x

Write the function for the following table:

• f(x) = 1(3)^x

• f(x) = 3(3)^x

• f(x) = 3x+3

• f(x)= 6x+1

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

Given the table in the image shown, what type of function does this table represent?

• Linear

• Quadratic

• Exponential

• Constant

Answer explanation

The table represents an exponential function because the values increase at an increasing rate, indicating a multiplicative growth pattern rather than a constant or linear change.

If the value of y doubles as x increases by 1, what is the base b of the exponential function y=ab^x?

• 3

• 1

• 2

• 0.5

Answer explanation

If y doubles when x increases by 1, we have y = ab^x and 2y = ab^(x+1). Dividing gives 2 = b, so the base b of the exponential function is 2.