1-5 Modeling with Exponential Functions

Determine whether a linear model or an exponential model would be most appropriate for the data.

• Linear

• Exponential

Determine whether a linear model or an exponential model would be most appropriate for the data.

• Linear

• Exponential

Calculate the average RATIO between successive y-values.

• ratio= 1.725

• ratio= 3.426

• ratio= 1.9

Calculate the average RATIO between successive y-values.

• ratio= 0.8

• ratio= 0.5

• ratio= 2.5

• 1.3

Calculate the average RATIO between successive y-values.

• ratio= 1.2

• ratio= 2.5

• ratio= 4.6

Identify whether the data shows exponential GROWTH or exponential DECAY. Then, determine an exponential function to model the situation.

• Exponential Growth; $y=62\left(1.75\right)^x$

• Exponential Growth; $y=62\left(1.34\right)^x$

• Exponential Decay; $y=62\left(1.75\right)^x$

• Exponential Decay; $y=62\left(1.34\right)^x$

Identify whether the data shows exponential GROWTH or exponential DECAY. Then, determine an exponential function to model the situation.

• Exponential Growth; $y=2200\left(3.39\right)^x$

• Exponential Growth; $y=7500\left(3.34\right)^x$

• Exponential Decay; $y=2200\left(3.39\right)^x$

Identify whether the data shows exponential GROWTH or exponential DECAY. Then, determine an exponential function to model the situation.

• Exponential Growth; $y=2200\left(0.53\right)^x$

• Exponential Growth; $y=28\left(0.53\right)^x$

• Exponential Decay; $y=61\left(0.53\right)^x$

• Exponential Decay; $y=292000\left(0.47\right)^x$

Use the data set to generate an exponential model.

•  $y=20,480\left(0.44\right)^x$  
  

•  $y=29,870\left(0.84\right)^x$ 

•  $y=29,870\left(2.2\right)^x$ 

•  $y=12,124\left(.25\right)^x$  

• The y-intercept, $14,585, represents the value of the car when Carla purchased it in 2011.

• The y-intercept, $20,480, represents the value of the car when Carla purchased it in 2009.
  

• The y-intercept, $29,870, represents the value of the car when Carla purchased it in 2007.