Exponential Functions

The attendance at the art museum at the New Year’s opening was 250 people. The attendance has been increasing at a rate of 3% each month. How many people will attend by the end of a year (12 months)?

Change growth rate to a decimal.
growth factor = 1 + growth rate

Which of the following is the correct exponential equation for this information?

 $\$  

• y=.03x + 250

•  $y=250\left(1+.03\right)^x$  
  

•  $y=3\left(250\right)^x$  

•  $y=250\left(1+3\right)^x$  

The attendance at the art museum at the New Year’s opening was 250 people. The attendance has been increasing at a rate of 3% each month. How many people will attend by the end of a year (12 months)?

• 356

• 265

• 5825

• 1329

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. 

Which is the correct exponential equation for this situation?

• $y=4000\left(1+.25\right)^x$

• $y=4000\left(1+25\right)^x$

• y=.25x + 4000

• $y=4000\left(1-.25\right)^x$

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

• 9766
• 9006
• 9765
• 5433

A colony of termites is growing continuously at a rate of 6.2% monthly. If the colony starts with 500, which equation correctly models this information?

• y=.062x + 500

• $y=500\left(1-.062\right)^x$

• y=.062x - 500

• $y=500\left(1+.062\right)^x$

A colony of termites is growing continuously at a rate of 6.2% monthly. If the colony starts with 500, how many would there be in one year?

• 1.02 E 35 (huge amount)
• 1052
• 246375
• 532

The equation for this table is 

• y = 25(4^x)
• y = 4(25^x)
• y = 4x
• y = 4^x

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

• y=6(0.14)^x
• y=6(1+14)^x
• y=6(1.14)^x
• y=6(0.86)^x

What is a, the initial amount, for the function: f(x) = 300(1.16)^x?

• 300
• 1.16
• .16
• x

A 78 gram sample of Uranium loses half of its mass each year.  What is the exponential equation? 

• y=78(0.5)^x
• y=78(1.5)^x
• y=78(2)^x