The monthly Medicare Part B healthcare premium for most beneficiaries ages $65$ and older has increased significantly since 1975. The monthly premium has increased from about $\$ 7$ in 1975 to $\$ 110.50$ in 2011. The following exponential function models the premium increases:

$$M(x)=7(1.080)^x,$$

where $x$ is the number of years since 1975. Estimate the monthly Medicare Part B premium in 1985, 1992, and 2002. Round to the nearest dollar.

Use a graphing calculator to find the approximate solutions of the equation. $\\$$4 x-3^x=-6$

Given that $\log _a 2=0.301, \log _a 5=0.699$, and $\log _a 6=0.778$, find each of the following. $\\$$\log _a \sqrt[3]{5}$

Simplify the exercise below: $\\$$\log _t t^{2713}$

For each function: $\\$ a) Determine whether it is one-to-one.$

$$b) If the function is one-to-one, find a formula for the inverse.$$

f(x)=2 x^2-x-1$

The number of pages in the IRS Tax Code has increased from $400$ pages in 1913 to $70,320$ pages in 2009. The increase can be modeled by the exponential function

$$T(x)=400(1.055)^x,$$

where $x$ is the number of years since 1913. Use this function to estimate the number of pages in the tax code for 1950, 1990, and for 2000. Round to the nearest one.

Simplify the exercise below: $\\$$\log _p p^3$

Given that $\log _a 2=0.301, \log _a 5=0.699$, and $\log _a 6=0.778$, find each of the following.

$\log _a \frac{1}{5}$

Use a graphing calculator to find the approximate solutions of the equation. $\\$$x e^{3 x}-1=3$

For each function: $\\$ a) Determine whether it is one-to-one.$ $$ b) If the function is one-to-one, find a formula for the inverse. $$ f(x)=x $$ \sqrt{4-x^2}$ $$

Find each of the following using a calculator. Round to four decimal places. $\\$$\ln 809.3$

Given that $\log _b 2 \approx 0.693, \log _b 3 \approx 1.099$, and $\log _b 5 \approx 1.609$, find each of the following, if possible. Round the answer to the nearest thousandth. $\\$$\log _b 15 b$

Find each of the following using a calculator. Round to four decimal places. $\\$$\ln (-4)$

For each function: $\\$ a) Determine whether it is one-to-one.$

$$b) If the function is one-to-one, find a formula for the inverse.$$

f(x)=(x+5)^3$