Exponential Functions with Tables

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

Tags

CCSS.HSF.IF.A.2

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

Tags

CCSS.HSF.LE.A.2

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.

Tags

CCSS.HSF-LE.A.1A

Left to right, what happens to the y-values?​ (a)   The table represents exponential ​ (b)   The decay factor (b-value) is (c)   ​

• They are multiplied by 1/3

• They are multiplied by 3

• 1/3

• decay

• 3

• growth

Answer explanation

The function f(x)=27(\frac{1}{3})^x represents exponential decay, which fits the table's values decreasing as x increases. The other options either represent linear functions or exponential growth, making them incorrect.

Tags

CCSS.HSF-LE.A.1A

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

Tags

CCSS.HSF.LE.A.2

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

Tags

CCSS.HSF.LE.A.2

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.

Tags

CCSS.HSF.LE.A.2

You are sick and your doctor prescribes a medication. One dose is 200 mg. Every half hour 30% of the medication leaves the body. You take the first dose at 6 am. If y = amount of medication in the body and x = a 30 minute interval, what equation fits the scenario?

• y=30(0.70)^x

• y=200(0.30)^x

• y=200(x)^0.3

• y=200(0.70)^x

Tags

CCSS.HSF.LE.A.2

You are given a penny. On day one it is tripled, along with every day after that. Write the equation for this scenario.

• y=0.01(3)^x

• y=0.01(x)³

• y=0.01(2)³

• y=0.01x+3

Tags

CCSS.HSF.LE.A.2