91Ó°ÊÓ

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I modeled California's population growth with a geometric sequence, so my model is an exponential function whose domain is the set of natural numbers.

$$ \text { Solve: } x^{4}-6 x^{3}+4 x^{2}+15 x+4=0 $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I used a formula to find the sum of the infinite geometric series \(3+1+\frac{1}{3}+\frac{1}{9}+\cdots\) and then checked my answer by actually adding all the terms.

Determine the amplitude, period, and phase shift of \(y=\frac{1}{2} \cos \left(3 x+\frac{\pi}{2}\right) .\) Then graph one period of the function. (Section 5.5, Example 6 )

will help you prepare for the material covered in the next section. Consider the sequence \(8,3,-2,-7,-12, \ldots . .\) Find \(a_{2}-a_{1}\) \(a_{3}-a_{2}, a_{4}-a_{3},\) and \(a_{5}-a_{4} .\) What do you observe?

In Exercises \(105-108\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If the \(n\) th term of a geometric sequence is \(a_{n}=3(0.5)^{n-1}\) the common ratio is \(\frac{1}{2}\)

will help you prepare for the material covered in the next section. Consider the sequence whose \(n\) th term is \(a_{n}=4 n-3\) Find \(a_{2}-a_{1}, a_{3}-a_{2}, a_{4}-a_{3},\) and \(a_{5}-a_{4} .\) What do you observe?

Use the formula \(a_{n}=4+(n-1)(-7)\) to find the eighth term of the sequence \(4,-3,-10, \ldots\)

You are now 25 years old and would like to retire at age 55 with a retirement fund of \(\$ 1,000,000 .\) How much should you deposit at the end of each month for the next 30 years in an IRA paying \(10 \%\) annual interest compounded monthly to achieve your goal? Round up to the nearest dollar.

Find the dimensions of a rectangle whose perimeter is 22 feet and whose area is 24 square feet. (Section \(8.4,\) Example 5 )