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
22x
4x
Blake (26 - 3)x
(23)x
23x
8x
Christine
29x
18x
Explain to Anna, Blake, and Christine who is correct, and identify any errors that you find. Provide the correct manner to fix those problems, and identify the correct answer. Use complete sentences. Anna’s work is correct. Blake made the mistake of subtracting 3, instead of multiplying 6 and X. Christine multiplied with 3; where as you are supposed to multiply with 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).
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If B is greater than one, it would be exponential. If one is larger than B, it would bw exponential decay.
X being the amount of years, which could be anything.
Domain x > - 0 or [0, infinity].
Range: [>0]
3. 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.
Year Population
3 159.181
4 162.365
5 165.612
To get the average rate of change, we get the three years’ worth of population, and subtract them
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Overflow occurs when the two numbers of similar signs are added together and a result with an opposite sign is produced.
2. Predict: How do you think the amount of land available will affect the rabbit population?
Daniel added the exponents in the denominator instead of multiplying them like he was supposed to. Daniel misused the Power of Powers rule because the rules state you multiply the two exponents and he added them. If he multiplied the two exponents he would've gotten the correct answer which is 6 as the exponent. He then should've subtracted 6 from 8 and he would've gotten the correct answer which is
The cohort component approach has three main components: births, deaths, and migration. The cohort component model uses these three components to move age/sex cohorts forward through time, creating a new age/sex distribution at each five-year time point. The success of the model depends on identifying appropriate fertility, mortality, and migration rates to apply to different age
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Use the distributive property to remove the parentheses in the following expression. Then simplify your result if possible.
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* Given linear and exponential data, interpret the rate of change within the given context.
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Even if you do the Math equation the same, the symbols can cause the answer to shift, and make it so the two aren’t the same.
Something to keep in mind is that linear functions and exponential functions are different. The first