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Solve the following exercises on a graphing calculator by graphing an appropriate exponential function (using \(x\) for ease of entry) together with a constant function and using INTERSECT to find where they meet. You will have to choose an appropriate window. GENERAL: Inflation At \(2 \%\) inflation, prices increase by \(2 \%\) compounded annually. How soon will prices: a. double? b. triple?

Find the derivative of each function. $$ f(z)=\frac{e^{z}}{z^{2}-1} $$

GE NERAL: Temperature A covered mug of coffee originally at 200 degrees Fahrenheit, if left for \(t\) hours in a room whose temperature is 70 degrees, will cool to a temperature of \(70+130 e^{-1.8 t}\) degrees. Find the temperature of the coffee after: a. 15 minutes. b. half an hour.

BEHAVIORAL SCIENCE: Learning In many psychology experiments the percentage of items that are remembered after \(t\) time units is $$ p(t)=100 \frac{1+e}{1+e^{t+1}} $$ Such curves are called "forgetting" curves. Find the percentage remembered after: a. 0 time units. b. 2 time units.

Find the derivative of each function. $$ f(z)=\frac{e^{z}}{1+e^{z}} $$

Solve the following exercises on a graphing calculator by graphing an appropriate exponential function (using \(x\) for ease of entry) together with a constant function and using INTERSECT to find where they meet. You will have to choose an appropriate window. GE NERAL: Inflation At \(5 \%\) inflation, prices increase by \(5 \%\) compounded annually. How soon will prices: a. double? b. triple?

In 1998 the State of New Jersey raised cigarette taxes, with the result that the price of a pack of cigarettes rose from $$\$ 2.40$$ to $$\$ 2.80$$. Demand then fell from 52 to \(47.5\) million packs. Use these data to estimate the elasticity of demand for cigarettes.

BIOMEDICAL: Epidemics The Reed-Frost model for the spread of an epidemic predicts that the number \(I\) of newly infected people is \(I=S\left(1-e^{-r x}\right)\), where \(S\) is the number of susceptible people, \(r\) is the effective contact rate, and \(x\) is the number of infectious people. Suppose that a school reports an outbreak of measles with \(x=10\) cases, and that the effective contact rate is \(r=0.01\). If the number of susceptibles is \(S=400\), use the Reed-Frost model to estimate how many students will be newly infected during this stage of the epidemic.

Solve the following exercises on a graphing calculator by graphing an appropriate exponential function (using \(x\) for ease of entry) together with a constant function and using INTERSECT to find where they meet. You will have to choose an appropriate window. PERSONAL FINANCE: Interest A bank account grows at \(6 \%\) compounded quarterly. How many years will it take to: a. double? b. increase by \(50 \%\) ?

Find the derivative of each function. $$ f(z)=\frac{10}{1+e^{-2 z}} $$