IM Unit 5 Lessons 7-9 QPC Retake Review

IM Unit 5 Lessons 7-9 QPC Retake Review

This review will walk you through how to determine....

1) if an equation is showing growth or decay

2) how to use your calculator to evaluate equations / function

3) interpreting exponents and their values

Calculator Usage

• to enter an exponent, you need to use the ^ button on you calculator

• for negative values, you need to be sure to use the (-) button...NOT THE SUBTRACTION button

Multiple Choice

What is the value of the equation when x = 5?

 $y\ =\ 6\left(\frac{1}{2}\right)^x$  

• 15

• 0.1875

Multiple Choice

What is the value of this function when x = -3?

 $f\left(x\right)\ =\ 6\left(\frac{1}{3}\right)^x$  

• 162

• 0.22

• I do not know, the calculator gave me an error

Did you get an error for the last question?

If so, then you used the subtraction symbol instead of the negative

( - ) button...it is down at the bottom of the calculator.

Open Ended

Let's try some more examples...
A person is considered to have an infection if 3,000,000 bacteria are present in a person's body. (this is not a real fact)
If the person is treated with antibiotics, only 3/5 of the bacteria remain each day. How many bacteria will there be after 3 days? Use this equation:

 $y\ =\ 3,000,000\left(\frac{3}{5}\right)^x$  

Open Ended

Let's try some more examples...
A person is considered to have an infection if 3,000,000 bacteria are present in a person's body. (this is not a real fact)
If the person is treated with antibiotics, only 3/5 of the bacteria remain each day. How many bacteria were there 2 days before the person went to the doctor? Use this equation:

 $y\ =\ 3,000,000\left(\frac{3}{5}\right)^x$  

Growth or Decay?

We need to look at the growth factors!

Here are examples of equations that model growth.  Notice that the growth factors all are greater than 1.  No calculations needed!

•  $y=2\left(5\right)^x$  

•  $y=8\left(1.05\right)^x$  

•  $y=5\left(\frac{4}{3}\right)^x$  

Here are examples of equations that model decay (the equation is decreasing).  Notice that the growth factors all are less than 1.  No calculations needed!

•  $y=2\left(\frac{1}{5}\right)^x$  

•  $y=8\left(0.2\right)^x$  

•  $y=5\left(\frac{4}{9}\right)^x$  

Multiple Choice

Is this exponential growth or decay?

• Growth

• Decay

Multiple Choice

What type of function is f(x)=2(1/7)^x ?

• Exponential Growth

• Linear

• Exponential Decay

• None of the Abovee

Multiple Choice

What type of function is y = 7(5/4)^x?

• Exponential Growth
• Exponential Decay
• Linear
• None of the above

Multiple Choice

What type of function is y = 7(2.6)^x?

• Exponential Growth

• Exponential Decay

• Linear

• None of the above

We can also tell from a graph.

Read graphs left to right...is it rising or falling?

Multiple Choice

Is this exponential growth or decay?

• Growth
• Decay
• Linear

Let's practice writing equations/functions.

Remember: y = (initial amount)(growth factor)^x and the exponent represents our time

Multiple Choice

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 5/3 a week.

• y=6(5/3)x

• y=(5/3)(6)^x

• y=6(5/3)^x

• y=6(2/3)^x

Multiple Choice

Which of the following functions shows an initial amount of $15 and an increase of 27/20 each year?

• y = 15(35)x

• y = 15(27/20)^x

• y = (27/20)(15)^x

• y = 35(7/20)^x

Multiple Choice

Suppose a culture of bacteria begins with 5000 cells and dies by 3/10 each year. Write an equation that represents this situation.

• y=5000(7/10)^x

• y=(7/10)(5000)^x

• y=5000^x

• y=5000(3/10)^x

Let's put it all together!

Multiple Choice

Daniel’s Print Shop purchased a new printer for $35,000. Each year 19/20 of its value remains. How much will the printer be worth in 8 years?

• $23,219.72

• $136.72

• $51,710.94

• $16,710.94

Multiple Choice

A population of fish starts at 8,000 and decreases by 1/5 per year. What is the population of fish after 10 years?

• 14327

• 859

• 839

• 7680

Multiple Choice

What is the growth factor in the following model?

A=1200(.85)⁶

• 1200

• -.15

• .85

• A