#### Transcript of module 4 quiz

zoey ramsay

1)Three of your friends, Anna, Blake, and Christine, run to you to settle a dispute. They were simplifying a radical expression into an exponential expression, but they reached different answers. Wisely, you decide to look at their work to see if you can spot the source of confusion.

Anna's work is correct. Blake subtracted 3 instead of multiplying 6 and x. Christine multiplied by 3 instead of 1/3.

2) Create an exponential growth function, f(x), to model a population of frogs that is growing every year. Identify the principal amount, the growth rate, and the appropriate domain and range for your function. Explain how these key features would affect the graph of f(x).

Here's a function: y = 200(1.03^4.

200 is the initial number of frogs

1.03 means that the number of frogs is increasing by 3% per year

and the 4 = # of years, 4 years

Therefore y gives you the total number of frogs after 4 years, if you were to start with 200 frogs and they increase by 3% per year.

1) Using your function f(x) from question 2. Demonstrate and explain how to find the average rate of change between year 3 and 5, and between year 5 and 7. Explain what the average rate of change represents to the frog population.

F(x) =150(1.02)^x

F(x) =150(1.02)^3

F(3) =150(1.02^3)

f(3) = 150(1.061208)

f(3) = 159.1812,

F(5) = 150(1.02)^5

166

F(7) = 150(1.02)^7

172

average rate of change formula is; \[\frac{ f(b) - f(a) }{b -a}\]

The length of a rectangular picture frame has been found to be an irrational number. Dwayne says that because the length is an irrational number, the perimeter and area would always be irrational. Using complete sentences, critique Dwayne’s statement with examples that demonstrate how he is correct or incorrect.

say the length is √(2) and width is 2√(2). Area would be 4, and 4 is a rational number.

**module 4 quiz**

module 4 quiz

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