Question

Math help

Answer 1

@Vocaloid or @dude pls check these whenever you get a chance

Answer 2

@dude

Answer 3

#3.png
The formula for compound interest is
\[A(t) = A_0(1 + r/n)^{nt}\] where \(A(t)\) is the amount after \(t\), years, \(A_0\) is the initial investment, \(r\) is the interest rate in decimal form, and \(n\) is the number of compounding periods per year. Here, \(A_0\) is the unknown.

We have the following information:

\(A(t) = 750\) dollars, \(t = 10 + 8/12 = 32/3\) years, because 10 years and 8 months, \(n = 365\) compounding periods per year since it is compounded daily, and \(r = 0.025\) as that is \(2 \frac{1}{2}\%\) in decimal form.

The formula becomes \[ 750 = A_0(1 + 0.025/365)^{365 \cdot 32/3} \] and we divide both sides in such a way that we isolate \(A_0\) to get \[A_0 = \frac{750}{(1 + 0.025/365)^{365 \cdot 32/3}} \approx \$574.45\] so we need to invest $574.45.

Answer 4

#5.png
This is the same story with \(A_0\) as the unknown with
\(t = 2+ 1/4 = 9/4\text{ years}\) as that is 2 and one-quarter years,
\(A(9/4) = 10500\), as that is the amount after 2 and one-quarter years,
\(n = 12\) since we have monthly compounding so 12 compounding periods a year, and
\(r = 0.0325\), as that is \(3 \frac{1}{4}\%\) in decimal form.

The formula becomes \[10500 = A_0(1 + 0.0325/12)^{12\cdot 9/4} \] and we solve for \(A_0\) to get \[A_0 = \frac{10500 }{(1 + 0.0325/12)^{12\cdot 9/4} } \approx \$9760.55\] so we need to invest $9760.55

Answer 5

#8.png
This is an exponential function the function is of the form \(f(x) = (b)^{x}\) where \(b>0\). So this does fit the form of an exponential function.