Exponential Regression

A box containing 1,000 coins is shaken, and the coins are emptied onto a table. Only the coins that land heads up are returned to the box, and then the process is repeated. The accompanying table shows the number of trials and the number of coins returned to the box after each trial.

Write an exponential regression equation that represents the table.

Mathematical Equivalence

ON

A box containing 1,000 coins is shaken, and the coins are emptied onto a table. Only the coins that land heads up are returned to the box, and then the process is repeated. The accompanying table shows the number of trials and the number of coins returned to the box after each trial.

Using the equation you wrote, predict how many coins would be returned to the box after the eighth trial.

Mathematical Equivalence

ON

The breaking strength, y, in tons, of steel cable with diameter d, in inches, is given in the table.

Write an exponential regression equation.

Round to the nearest hundredth

Mathematical Equivalence

ON

The breaking strength, y, in tons, of steel cable with diameter d, in inches, is given in the table.

Use the equation you got to predict how many tons a cable with a diameter of 5 inches could hold.

Mathematical Equivalence

ON

The accompanying table shows the number of bacteria present in a certain culture over a 5-hour period, where x is the time, in hours, and y is the number of bacteria.

 Write an exponential regression equation.

Round to the nearest hundredth.

Mathematical Equivalence

ON

The accompanying table shows the number of bacteria present in a certain culture over a 5-hour period, where x is the time, in hours, and y is the number of bacteria.

 Using this equation you wrote, determine the number of whole bacteria present when x equals 6.5 hours.

Round to the nearest hundredth.

Mathematical Equivalence

ON

Determine the y-intercept and asymptote for the following exponential function.

Hint: for the asymptote , just click which dot it would be, BE CAREFUL on this one!

What is the equation that models the data in the table?

Use the formula: y=a(b)^x

• y = 3(3)^x

• y = 3^x

In March, 2020, before the Covid-19 lockdown, 1,200,000 Texans had applied for unemployment. During the COVID-19 lockdown, the number of people applying for unemployment increased by 4% each month. What exponential function can be used to find the number of people applying for unemployment after x months of COVID-19 lockdown?​ (a)