Question

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Problems 1-6

1.) Thalia is currently 104 cm tall, and the doctor tells her she can expect to grow at 2.2 cm per year for the foreseeable future. What is the function rule (equation) for this scenario?
2.) In the problem above, identify the linear function's parameters.
3.) The 2011 population of manatees in Florida was 5,067. The animal is thought to be experiencing annual exponential decay of 1.1%. What is the function rule for this scenario?
4.) In the problem above, identify the exponential function's parameters (the independent and dependent variables).
5.) Does problem 3 describe growth or decay? Why? Use a complete sentence.
6.) What is the growth or decay rate in problem 3?

Answer 1

1.) The function rule (equation) for Thalia's height over time can be modeled as h(t) = 104 + 2.2t, where h(t) is her height in cm at time t in years.

2.) In the equation for Thalia's height, 104 is the y-intercept and 2.2 is the slope.

3.) The function rule for the manatee population in Florida can be modeled as P(t) = P0 * 0.989^t, where P(t) is the population at time t in years and P0 is the initial population (5,067).

4.) In the equation for the manatee population, P0 is the initial population and 0.989 is the decay rate. The independent variable is t (time in years) and the dependent variable is P (population).

5.) Problem 3 describes decay. This is because the population of manatees in Florida is decreasing at a constant rate of 1.1% per year.

6.) The growth or decay rate in problem 3 is -1.1%.

Explanation:

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Answer 2

Answer:The function rule for Thalia's height (h) in years (t) is h(t) = 104 + 2.2t.

The linear function's parameters are: h0 = 104 (initial height), and k = 2.2 (the rate of growth in cm per year).

The function rule for the population of manatees (P) in years (t) is P(t) = 5,067 * (1.011)^(-t), where t is the number of years passed since 2011.

The exponential function's parameters are: P0 = 5,067 (the initial population), t (the number of years passed since 2011), and k = 0.011 (the decay rate).

Problem 3 describes decay. The population of manatees is decreasing by a certain percentage each year, indicating a decrease in the number of animals over time.

The decay rate in problem 3 is 1.1% (or 0.011 in decimal form).

Explanation: