91Ó°ÊÓ

Iodine-131 has a decay rate of \(9.6 \%\) per day. The rate of change of an amount \(N\) of iodine- 131 is given by \(\frac{d N}{d t}=-0.096 N\) where \(t\) is the number of days since the decay began. a) Let \(N_{0}\) represent the amount of iodine-131 present at \(t=0 .\) Find the exponential function that models the situation. b) Suppose that \(500 \mathrm{g}\) of iodine- 131 is present at \(t=0\) How much will remain after 4 days? c) After how many days will half of the 500 g of iodine-131 remain?

For the demand function given in each,Find the following. a) The elasticity b) The elasticity at the given price, stating whether the demand is elastic or inelastic c) The value(s) of \(x\) for which total revenue is \(a\) maximum (assume that \(x\) is in dollars) $$q=D(x)=500-x ; \quad x=38$$

Write an equivalent exponential equation. $$\log _{3} 81=4$$

Write an equivalent exponential equation. $$-\log _{b} V=w$$

Write an equivalent logarithmic equation. $$10^{3}=1000$$

Euler Bank advertises that it compounds interest continuously and that it will double your money in 15 yr. What is its annual interest rate?

Sunshine Gardens determines the following demand function during early summer for tomato plants: $$q=D(x)=\frac{2 x+300}{10 x+11}$$ where \(q\) is the number of plants sold per day when the price is \(x\) dollars per plant. (GRAPH CANNOT COPY) a) Find the elasticity. b) Find the elasticity when \(x=3\) c) At $$ 3$ per plant, will a small increase in price cause the total revenue to increase or decrease?

Given \(\log _{b} 3=1.099\) and \(\log _{b} 5=1.609,\) find each value. $$\log _{b} \sqrt{b^{3}}$$

The supply and demand for stereos produced by a sound company are given by $$S(x)=\ln x \quad \text { and } \quad D(x)=\ln \frac{163,000}{x}$$ where \(S(x)\) is the number of stereos that the company is willing to sell at price \(x\) and \(D(x)\) is the quantity that the public is willing to buy at price \(x\). Find the equilibrium point. (See Section R.5.)

Differentiate. $$F(x)=-\frac{2}{3} e^{x^{2}}$$