91Ó°ÊÓ

Find each of the following, to four decimal places, using a calculator. $$e^{4}$$

Find the inverse of the relation. $$\\{(0,1),(5,6),(-2,-4)\\}$$

Solve the exponential equation algebraically. Then check using a graphing calculator. Round to three decimal places, if appropriate. $$3^{7 x}=27$$

The population of Haiti has a growth rate of \(1.08 \%\) per year. In \(2015,\) the population was \(9,996,731,\) and the land area of Haiti is \(32,961,561,600\) square yards. (Source: U.S. Census Bureau)(IMAGE CAN'T COPY)Assuming that this growth rate continues and is exponential, after how long will there be one person for every square yard of land?

Solve the exponential equation algebraically. Then check using a graphing calculator. Round to three decimal places, if appropriate. $$10^{-x}=5^{2 x}$$

Graph the function by substituting and plotting points. Then check your work using a graphing calculator. $$f(x)=3^{-x}$$

Solve the exponential equation algebraically. Then check using a graphing calculator. Round to three decimal places, if appropriate. $$e^{-c}=5^{2 c}$$

Newton's Law of Cooling. Suppose that a body with temperature \(T_{1}\) is placed in surroundings with temperature \(T_{0}\) different from that of \(T_{1}\). The body will either cool or warm to temperature \(T(t)\) after time \(t,\) in minutes, where $$T(t)=T_{0}+\left(T_{1}-T_{0}\right) e^{-i t}$$,A cup of coffee with temperature \(105^{\circ} \mathrm{F}\) is placed in a freezer with temperature \(0^{\circ} \mathrm{F}\). After \(5 \mathrm{min}\), the temperature of the coffee is \(70^{\circ} \mathrm{F}\). What will its temperature be after 10 min?

Newton's Law of Cooling. Suppose that a body with temperature \(T_{1}\) is placed in surroundings with temperature \(T_{0}\) different from that of \(T_{1}\). The body will either cool or warm to temperature \(T(t)\) after time \(t,\) in minutes, where $$T(t)=T_{0}+\left(T_{1}-T_{0}\right) e^{-i t}$$,A chilled gelatin salad that has a temperature of \(43^{\circ} \mathrm{F}\) is taken from the refrigerator and placed on the dining room table in a room that is \(68^{\circ} \mathrm{F}\). After \(12 \mathrm{min}\), the temperature of the salad is \(55^{\circ} \mathrm{F}\). What will the temperature of the salad be after 20 min?

Newton's Law of Cooling. Suppose that a body with temperature \(T_{1}\) is placed in surroundings with temperature \(T_{0}\) different from that of \(T_{1}\). The body will either cool or warm to temperature \(T(t)\) after time \(t,\) in minutes, where $$T(t)=T_{0}+\left(T_{1}-T_{0}\right) e^{-i t}$$When Was the Murder Committed? The police discover the body of a murder victim. Critical to solving the crime is determining when the murder was committed. The coroner arrives at the murder scene at 12: 00 P.M. She immediately takes the temperature of the body and finds it to be \(94.6^{\circ} \mathrm{F}\). She then takes the temperature 1 hr later and finds it to be \(93.4^{\circ} \mathrm{F}\). The temperature of the room is \(70^{\circ} \mathrm{F}\). When was the murder committed?