A city's population is 1000 and growing at $5\%$ a year.Find a formula for the population at time $t$ years from now assuming that the $5\%$ per year is an:
(i) Annual rate (ii) Continuous annual rate

Consider a semi cylindrical trough of radius R and length L. Develop general expressions for the magnitude and line of action of the hydrostatic force on one end, if the trough is partially filled with water and open to atmosphere. Plot the results (in non dimensional form) over the range of water depth $0 \leq \mathrm{d} / \mathrm{R} \leq 1$.

Perform the indicated operation and, if possible, simplify.

$$\frac{a}{6 a-9 b}-\frac{b}{4 a-6 b}$$

How to calculate the boiling point of water at different pressures?

3. In the figure below, point Z is the image of point X resulting from successive reflections through parelle! lines, /, and /,. a - 11 Ne ee $\mathscr { A }$ a) Label the distance from X to /, 2 and the distance from ¥ to i, &. Also label the distances from Y to |, and Z to i, in terms of aand b.

p) What is the distance between !, and f, in terms of @ and bb?

Perform the indicated operation

$$\left(w^6-w^3\right)-\left(-w^2+w\right)$$

At fast-food restaurants, the lids for drink cups are made with a small amount of flexibility, so they can be stretched across the mouth of the cup and then snugly secured. When lids are too small or too large, customers can get frustrated, especially if they end up spilling their drinks. At one restaurant, large drink cups require lids with a diameter of between 3.95 and 4.05 inches. The restaurant's lid supplier claims that the diameter of the large lids follows a normal distribution with mean 3.98 inches and standard deviation 0.02 inches. Assume that the supplier's claim is true.

What percent of large lids have diameters between 3.95 and 4.05 inches?

Name the operation that should be performed first. Do not perform the calculation.

7-9+15

Perform the indicated operation and write the result in standard form.

$$\sqrt { - 81 } - \sqrt { - 144 }$$

For the following problem, write an equation for the inverse relation by interchanging the variables and solving for y in terms of x. Then plot the function and its inverse on the same screen, using function mode. Sketch the result, showing that the function and its inverse are reflections across the line y = x. Tell whether or not the inverse relation is a function.

$$y=-0.5 x^2-2$$

For the following exercise, use the compound interest formula, $A(t)=P\left(1+\frac{r}{n}\right)^{n t}$.
Use the formula found in the previous exercise to calculate the interest rate for an account that was compounded semi-annually, had an initial deposit of $\$ 9,000$ and was worth $\$ 13,373.53$ after 10 years.

At higher altitudes, water boils at lower temperatures. This relationship between altitude and boiling point is linear. At an altitude of 1000 feet, water boils at

$$210 ^ { \circ } \mathrm { F }$$

. At an altitude of 3000 feet, water boils at

$$206 ^ { \circ } \mathrm { F }$$

. Write an equation in slope-intercept form that represents this linear function. Then find the boiling point at 6000 feet.

Distance to an airplane A straight road makes an angle of $22^{\circ}$ with the horizontal. From a certain point $P$ on the road, the angle of elevation of an airplane at point $A$ is $57^{\circ}$. At the same instant, from another point $Q, 100$ meters farther up the road, the angle of elevation is $63^{\circ}$. As indicated in the figure, the points $P, Q$, and $A$ lie in the same vertical plane. Approximate the distance from $P$ to the airplane.

On May 1, Jennings, a car dealer, e-mails Wheeler and says, “I have a 1955 Thunderbird convertible in mint condition that I will sell you for $13,500 at any time before June 9. [Signed] Peter Jennings.” By May 15, having heard nothing from Wheeler, Jennings sells the car to another. On May 29, Wheeler accepts Jennings’s offer and tenders$13,500. When told Jennings has sold the car to another, Wheeler claims Jennings has breached their contract. Is Jennings in breach? Explain.