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Magazine Problem 295
Use the change-of-base formula and either base 10 or base \(e\) to evaluate the given expressions. Answer in exact form and in approximate form, rounding to four decimal places. \(\log _{0.5} 211\)
Problem 296
For the following exercises, use the change-of-base formula and either base 10 or base \(e\) to evaluate the given expressions. Answer in exact form and in approximate form, rounding to four decimal places. $$ \log _{2} \pi $$
Problem 296
Use the change-of-base formula and either base 10 or base \(e\) to evaluate the given expressions. Answer in exact form and in approximate form, rounding to four decimal places. \(\log _{2} \pi\)
Problem 297
Use the change-of-base formula and either base 10 or base \(e\) to evaluate the given expressions. Answer in exact form and in approximate form, rounding to four decimal places. \(\log _{0.2} 0.452\)
Problem 297
For the following exercises, use the change-of-base formula and either base 10 or base \(e\) to evaluate the given expressions. Answer in exact form and in approximate form, rounding to four decimal places. $$ \log _{0.2} 0.452 $$
Problem 298
Rewrite the following expressions in terms of exponentials and simplify. a. 2 \(\cosh (\ln x)\) b. \(\cosh 4 x+\sinh 4 x\) c. \(\cosh 2 x-\sinh 2 x\) d. \(\ln (\cosh x+\sinh x)+\ln (\cosh x-\sinh x)\)
Problem 299
The number of bacteria \(N\) in a culture after \(t\) days can be modeled by the function \(N(t)=1300 \cdot(2)^{t / 4}\). Find the number of bacteria present after 15 days.
Problem 299
[Tl] The number of bacteria \(N\) in a culture after \(t\) days can be modeled by the function \(N(t)=1300 \cdot(2)^{t / 4}\) . Find the number of bacteria present after 15 days.
Problem 300
[T] The demand \(D\) (in millions of barrels) for oil in an oil-rich country is given by the function \(D(p)=150 \cdot(2.7)^{-0.25 p}\) where \(p\) is the price (in dollars) of a barrel of oil. Find the amount of oil demanded (to the nearest million barrels) when the price is between \(\$ 15\) and \(\$ 20 .\)
Problem 300
The demand \(D\) (in millions of barrels) for oil in an oil-rich country is given by the function \(D(p)=150 \cdot(2.7)^{-0.25 p},\) where \(p\) is the price (in dollars) of a barrel of oil. Find the amount of oil demanded (to the nearest million barrels) when the price is between $$\$ 15$$ and $$\$ 20$$.
