91Ó°ÊÓ

Find the accumulated present value of each continuous income stream at rate \(R(t),\) for the given time \(T\) and interest rate \(k\) compounded continuously. $$R(t)=\$(2000 t+7), \quad T=30 \mathrm{yr}, \quad k=4.5 \%$$

Explain why both consumers and producers feel good when consumer and producer surpluses exist.

Let \(x\) be a continuous random variable with a standard normal distribution. Using Table A, find each of the following. $$ P(-2.45 \leq x \leq-1.24) $$

Determine whether each improper integral is convergent or divergent, and find its value if it is convergent. $$ \int_{0}^{\infty} m e^{-m x} d x, m>0 $$

Determine whether each improper integral is convergent or divergent, and find its value if it is convergent. $$ \int_{0}^{\infty} Q e^{-k t} d t, k>0 $$

Find the volume generated by rotating the area bounded by the graphs of each set of equations around the \(y\) -axis. $$ y=3 x, x=0, x=5 $$

Find \(k\) such that each function is a probability density function over the given interval. Then write the probability density function. $$ f(x)=k(4-x), \quad[0,4] $$

Find the accumulated present value of each continuous income stream at rate \(R(t),\) for the given time \(T\) and interest rate \(k\) compounded continuously. $$ R(t)=\$ t^{2}, \quad T=40 \mathrm{yr}, \quad k=4.25 \% $$

(a) find the general solution of each differential equation, and (b) check the solution by substituting into the differential equation. \(\frac{d h}{d t}=0.023 h\)

Let \(x\) be a continuous random variable with a standard normal distribution. Using Table A, find each of the following. $$ P(-1.27 \leq x \leq-0.58) $$