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Magazine Problem 5
The population of a certain city was 112,000 in 1998, and the observed relative growth rate is 4% per year. (a) Find a function that models the population after \(t\) years. (b) Find the projected population in the year 2004. (c) In what year will the population reach 200,000?
Problem 5
Evaluate the expression. $$ \log _{4} 192-\log _{4} 3 $$
Problem 5
5鈥�10 ? Sketch the graph of the function by making a table of values. Use a calculator if necessary. $$ f(x)=2^{x} $$
Problem 6
\(3-8\) Express the equation in exponential form. $$ \begin{array}{ll}{\text { (a) } \log _{3} 81=4} & {\text { (b) } \log _{8} 4=\frac{2}{3}}\end{array} $$
Problem 6
The frog population in a small pond grows exponentially. The current population is 85 frogs, and the relative growth rate is 18% per year. (a) Find a function that models the population after \(t\) years. (b) Find the projected population after 3 years. (c) Find the number of years required for the frog population to reach 600.
Problem 6
5鈥�10 ? Sketch the graph of the function by making a table of values. Use a calculator if necessary. $$ g(x)=8^{x} $$
Problem 6
Evaluate the expression. $$ \log _{12} 9+\log _{12} 16 $$
Problem 6
Find the solution of the exponential equation, correct to four decimal places. $$ 3^{2 x-1}=5 $$
Problem 7
Find the solution of the exponential equation, correct to four decimal places. $$ 3 e^{x}=10 $$
Problem 7
5鈥�10 ? Sketch the graph of the function by making a table of values. Use a calculator if necessary. $$ f(x)=\left(\frac{1}{3}\right)^{x} $$
