125: Exponential from 2 points

Bell:

1

What is the percent of growth:
y=12.5(1.03)^x

1

What is the percent of decay?
y=5.2\left(0.85\right)^x

Notes: Using 2 points to write an Exponential
We are using the form: y=a(b)^x

1

What does a mean?

1

Which point would give you the a value?

1

Write an exponential function in the form y=a(b)^x that goes through points (0,4) and (6,2916).

rhetorical q: What is a?

Write an equation that uses y=a(b)^x. The only variable that should be left is b.

1

Solve [5] for b.

1

Write the function that [5] requested.

1

Write an exponential function in the form y=a(b)^x that goes through points (0,9) and (3,4608).

rhetorical q: What is a?
Use the show your work space to write an equation that uses y=a(b)^x, and solve for b.

What is b?

1

Write the function that [8] requested.

1

Write an exponential function in the form y=a(b)^x that goes through points (0,19) and (4,1539).

rhetorical q: What is a?
Use the show your work space to write an equation that uses y=a(b)^x, and solve for b.

Write the function requested.

1

Sofia purchased a new car in 2007 for \$34,000. The value of the car has been depreciating exponentially at a constant rate.
If the value of the car was \$16,200 in the year 2014, then what would be the predicted value of the car in the year 2021, to the nearest dollar?
We are still using y=a(b)^x. Use the steps shown below:
What is a?
Find b.
Write a funtion.
Answer the question as stated.

1

The population of rabbits on an island is growing exponentially. In the year 2004, the population of rabbits was 490, and by 2008 the population had grown to 560. Predict the population of rabbits in the year 2014, to the nearest whole number.

0

Choose all that are true

You can now do the first two sections of DeltaMath.

125: Exponential from 2 points

Bell:

What is the percent of growth:y=12.5(1.03)^x

What is the percent of decay?y=5.2\left(0.85\right)^x

Notes: Using 2 points to write an Exponential

We are using the form: y=a(b)^x

What does a mean?

Which point would give you the a value?

Write an exponential function in the form y=a(b)^x that goes through points (0,4) and (6,2916).rhetorical q: What is a?Write an equation that uses y=a(b)^x. The only variable that should be left is b.

Solve [5] for b.

Write the function that [5] requested.

Write an exponential function in the form y=a(b)^x that goes through points (0,9) and (3,4608).rhetorical q: What is a?Use the show your work space to write an equation that uses y=a(b)^x, and solve for b.What is b?

Write the function that [8] requested.

Write an exponential function in the form y=a(b)^x that goes through points (0,19) and (4,1539).rhetorical q: What is a?Use the show your work space to write an equation that uses y=a(b)^x, and solve for b.Write the function requested.

The population of rabbits on an island is growing exponentially. In the year 2004, the population of rabbits was 490, and by 2008 the population had grown to 560. Predict the population of rabbits in the year 2014, to the nearest whole number.

Choose all that are true

Bell:

What is the percent of growth:y=12.5(1.03)^x

What is the percent of decay?y=5.2\left(0.85\right)^x

Notes: Using 2 points to write an Exponential

We are using the form: y=a(b)^x

What does a mean?

Which point would give you the a value?

Write an exponential function in the form y=a(b)^x that goes through points (0,4) and (6,2916).rhetorical q: What is a?Write an equation that uses y=a(b)^x. The only variable that should be left is b.

Solve [5] for b.

Write the function that [5] requested.

Write an exponential function in the form y=a(b)^x that goes through points (0,9) and (3,4608).rhetorical q: What is a?Use the show your work space to write an equation that uses y=a(b)^x, and solve for b.What is b?

Write the function that [8] requested.

Write an exponential function in the form y=a(b)^x that goes through points (0,19) and (4,1539).rhetorical q: What is a?Use the show your work space to write an equation that uses y=a(b)^x, and solve for b.Write the function requested.

The population of rabbits on an island is growing exponentially. In the year 2004, the population of rabbits was 490, and by 2008 the population had grown to 560. Predict the population of rabbits in the year 2014, to the nearest whole number.

Choose all that are true

What is the percent of growth:
y=12.5(1.03)^x

What is the percent of decay?
y=5.2\left(0.85\right)^x

Write an exponential function in the form y=a(b)^x that goes through points (0,4) and (6,2916).

rhetorical q: What is a?

Write an equation that uses y=a(b)^x. The only variable that should be left is b.

Write an exponential function in the form y=a(b)^x that goes through points (0,9) and (3,4608).

rhetorical q: What is a?
Use the show your work space to write an equation that uses y=a(b)^x, and solve for b.

What is b?

Write an exponential function in the form y=a(b)^x that goes through points (0,19) and (4,1539).

rhetorical q: What is a?
Use the show your work space to write an equation that uses y=a(b)^x, and solve for b.

Write the function requested.

What is the percent of growth:
y=12.5(1.03)^x

What is the percent of decay?
y=5.2\left(0.85\right)^x

Write an exponential function in the form y=a(b)^x that goes through points (0,4) and (6,2916).

rhetorical q: What is a?

Write an equation that uses y=a(b)^x. The only variable that should be left is b.

Write an exponential function in the form y=a(b)^x that goes through points (0,9) and (3,4608).

rhetorical q: What is a?
Use the show your work space to write an equation that uses y=a(b)^x, and solve for b.

What is b?

Write an exponential function in the form y=a(b)^x that goes through points (0,19) and (4,1539).

rhetorical q: What is a?
Use the show your work space to write an equation that uses y=a(b)^x, and solve for b.

Write the function requested.