How many years will it take to save $10,000 if he uses Bank A?

How many years will it take to save $10,000 if he uses Bank B?

[math]1,\frac{2}{3},\frac{4}{9},\frac{8}{27},\frac{16}{81},\dots[/math]

[math]3,\frac{6}{3},\frac{12}{9},\frac{24}{27},\frac{48}{81},\dots[/math]

[math]4,2,1,\frac{1}{2},\frac{1}{4},\dots[/math]

[size=150]Diego wonders how much money he could save over 25 years if he puts $150 a year into an account with 4% interest per year compounded annually. He calculates the following, but thinks he must have something wrong, since he ended up with a very small amount of money:[br][/size][br][math]\text{total amount}=150\frac{1-0.04^{25}}{0.96}=156.25[/math][br][br]What did Diego forget in his calculation?

How much should his total amount be? Explain or show your reasoning.

[size=150]Which one of these equations is equivalent to [math]8=\frac{3+2x}{4+x}[/math] for [math]x\ne\text{-}4[/math]?[/size]

[size=150]Is [math]a^3+b^3=(a+b)(a^2-ab+b^2)[/math] an identity? [br][/size]Explain or show your reasoning.

[size=150]Is [math]a^4+b^4=(a+b)(a^3-a^2b-ab^2+b^3)[/math] an identity?[/size] [br]Explain or show your reasoning.

The formula for the sum [math]s[/math] of the first [math]n[/math] terms in a geometric sequence is given by [math]s=a\left(\frac{1-r^n}{1-r}\right)[/math], where [math]a[/math] is the initial value and [math]r[/math] is the common ratio.[br][br]A medicine is prescribed for a patient to take 700 mg every 12 hours for 5 days. After 12 hours, 4% of the medicine is still in the body. How much of the medicine is in the body after the last dose?