91Ó°ÊÓ

If \(9^{x}=25,\) what does \(3^{x}\) equal?

Solve each equation. $$ \log _{2}(3 x+4)=5 $$

Find an exponential function whose graph has the horizontal asymptote \(y=2\) and contains the points (0,3) and \((1,5) .\)

Find an exponential function whose graph has the horizontal asymptote \(y=-3\) and contains the points (0,-2) and (-2,1).

Solve each equation. $$ \log _{5} 625=x $$

Can a one-to-one function and its inverse be equal? What must be true about the graph of \(f\) for this to happen? Give some examples to support your conclusion.

Solve each equation. $$ \log _{5}\left(x^{2}+x+4\right)=2 $$

Solve each equation. $$ \log _{2} 8^{x}=-6 $$

The normal healing of wounds can be modeled by an exponential function. If \(A_{0}\) represents the original area of the wound and if \(A\) equals the area of the wound, then the function $$ A(n)=A_{0} e^{-0.35 n} $$ describes the area of a wound after \(n\) days following an injury when no infection is present to retard the healing. Suppose that a wound initially had an area of 100 square millimeters. (a) If healing is taking place, how large will the area of the wound be after 3 days? (b) How large will it be after 10 days?

The relative humidity is the ratio (expressed as a percent) of the amount of water vapor in the air to the maximum amount that the air can hold at a specific temperature. The relative humidity, \(R\), is found using the following formula: $$ R=10^{\left(\frac{4221}{T+459.4}-\frac{4221}{D+459.4}+2\right)} $$ where \(T\) is the air temperature (in \({ }^{\circ} \mathrm{F}\) ) and \(D\) is the dew point temperature (in \(\left.^{\circ} \mathrm{F}\right)\) (a) Determine the relative humidity if the air temperature is \(50^{\circ}\) Fahrenheit and the dew point temperature is \(41^{\circ}\) Fahrenheit. (b) Determine the relative humidity if the air temperature is \(68^{\circ}\) Fahrenheit and the dew point temperature is \(59^{\circ}\) Fahrenheit. (c) What is the relative humidity if the air temperature and the dew point temperature are the same?