Hey dudes, I need my answers and reasoning checked. (uwu)
"Suppose you start with 24 rabbits, Each year they grow to 10 times as many! Write an exponential function to represent the rabbit population, y, based on the number of years that passed, x. Describe what the variables represent and how you built your equation."
I wrote this;
Function : y = 1*24^10
Definition : x = the number of years that passed ,
y = rabbit population ,
t = population growth after 1 year ,
1 = initial number of rabbits.
————————————————————————
"Let’s say this rabbit population pushes out the native chipmunk population, taking over their natural habitat. Suppose we started with 750,000 chipmunks and each year they are losing one third (1/3) of their population. Write an equation for this scenario."
Would the equation have to be formatted like: "y = a(1 - r)^x"? I don’t really understand exponential decay and my class hasn’t covered on that topic as much, any tips on that would be appreciated. (uwu)
24*10^x
your decay formula is correct. 1-r is the constant ratio to multiply by
Hey there! Let's go through your answers and reasoning step by step to check them:
1. For the first question, you need to write an exponential function to represent the rabbit population. You correctly identified the variables as x for the number of years that passed and y for the rabbit population. However, the function you wrote, y = 1*24^10, is not correct.
To represent the exponential growth of the rabbit population, you want to use the formula y = a * (b^x), where a is the initial number of rabbits and b is the rate at which the population grows. In this case, the rabbits grow to 10 times as many each year. So, you can set a = 24 (the initial number of rabbits) and b = 10. Therefore, the correct exponential function for the rabbit population would be:
y = 24 * (10^x)
In this equation, x represents the number of years that have passed, and y represents the rabbit population.
2. Now let's move on to the second question about the chipmunk population. You are correct that this scenario involves exponential decay. The general formula for exponential decay is y = a * (1 - r)^x, where a is the initial quantity, r is the decay rate, and x is the number of time periods.
In this case, the initial number of chipmunks is 750,000, and each year they are losing one-third (1/3) of their population. Since they are losing a fraction of their population each year, the decay rate (r) would be 1/3.
Therefore, the correct equation for the chipmunk population would be:
y = 750,000 * (1 - 1/3)^x
In this equation, x represents the number of years that have passed, and y represents the chipmunk population.
Regarding your question about exponential decay, it represents the decreasing value of a quantity over time. In this scenario, as the number of years increases, the chipmunk population decreases at a constant rate of one-third (1/3) of its current population.
I hope this helps! Let me know if you have any further questions.