Let's answer each of your questions one by one.
Question 1: Exponential Growth Equation
The growth of the wasp population can be modeled by the equation: w(t) = 5000(1.13)^t where w(t) is the number of wasps after t months. Thus, the correct answer is:
- w(t) = 5000(1.13)^t where w(t) is the number of wasps after t months
Question 2: Growth Behavior
The statement that is true about the wasp equation is:
- As t increases, w increases slowly at first and then quickly.
Question 3: 5th Term of the Sequence
To find the 5th term using the formula f(n) = 2n - 1:
- f(5) = 2(5) - 1 = 10 - 1 = 9. Thus, f(5) = 9.
Question 4: 11th Term of the Arithmetic Sequence
To find the 11th term using the formula A(n) = 4.8 + (n - 1)2:
- A(11) = 4.8 + (11 - 1) × 2 = 4.8 + 10 × 2 = 4.8 + 20 = 24.8. Thus, A(11) = 24.8.
Question 5: Manuel's Savings After a Year
Manuel has saved $253.32 and plans to put $50 into his savings each month for 12 months:
- Total savings after one year = $253.32 + (50 × 12) = $253.32 + $600 = $853.32. Thus, Manuel will have $853.32 after a year of savings.
Question 6: Growth Rates of Two Functions
Without seeing the actual growth rates in the table, a general statement that could often be true in such scenarios would be:
- While the growth rate of f(x) is initially greater than the growth rate of g(x), the growth rate of g(x) keeps increasing and eventually surpasses the growth rate of f(x). However, confirm by comparing the sequences.
Question 7: Recursive Function
For the sequence 41, 29, 17, 5, we can see that each term decreases by 12:
- The recursive function is An = An−1 − 12, A1 = 41.
Question 8: Function Representing Exponential Decay
The function that represents exponential decay has a base between 0 and 1:
- y = 3(0.5)^x represents exponential decay.
If you need further clarifications or assistance, feel free to ask!