Exam 4: Living in a Nonlinear World

In 2000, the population of Sheboygan, WI was about 113,000 and was growing at a rate of 0.85% per year. Find an exponential function that describes the population P in terms of t, the number of years after 2000.

The number of miles that light travels in one year is called a light-year, which is equal to The nearest start (other than the sun) to the earth is Proxima Centauri, at 4.2 light-years away. How far is that in miles?

If a bank compounds interest monthly for years, how many total compound periods are there?

Simplify.

Simplify. Write the answer with positive exponents only.

Factor completely. $a ^ { 2 } + 3 a b - 8 b ^ { 2 }$

Multiply the polynomials.

Use the distance formula to find the distance between the two points.

Find all values of k so that the distance from (8, -5)to (11, k)is 5 units.

Write the number in scientific notation. 483,000,000

Write the equation in the form $a x ^ { 2 } + b x + c = 0$ Then identify the values of a, b , and c . -9 x(8 x+9)=4 x

Find the total amount for the investment using compound interest.

Subtract the polynomials.

Simplify the expression. Write the answer in exponent form.

Factor completely.

Subtract the polynomials. $\left( \frac { 15 } { 2 } y ^ { 3 } + 2 y - \frac { 1 } { 4 } \right) - \left( 2 y ^ { 3 } - 8 y ^ { 2 } + \frac { 27 } { 2 } \right)$

In a right triangle, one leg measures 48 meters and the hypotenuse measures 52 meters. Find the length of the unknown leg.

Factor completely. $m ^ { 2 } + 4 m - 96$

Graph the function $f ( x ) = 3 ^ { x + 2 }$ . Plot at least three points.

Find the length of the unknown side.