precalc homework

Math 121 HW4 Due Tuesday, October 2 We will start penalizing students for improperly uploaded homework so please watch the video to help you do it properly. This homework set requires a calculator. Exam questions will not. Be certain to show all work.

1. $5000 is invested in an account paying 3.2% annually, compounded continuously.

a. How much money is in the account after at the end of 10 years? Round to the nearest penny.

b. How much time must pass before there is $9000 in the account?

Round the number of years to one decimal place.

2. $10,000 is invested in an account where the interest is compounded continuously. The investor hopes to have $16,000 in the account at the end of 12 years. Find the annual interest rate needed.

3. A species of insect is introduced into a new environment. The population is

defined by P t( ) = 10,000

20+30e−0.2t where t is the number of days and P is the

number of insects. a. How many insects were initially present?

b. How many days must pass before there are 400 insects present?

c. As t →∞ , what does the population of insects go to?

4. A sector has a central angle of 40o and a radius of 36mm. a. Find the area of the sector.

b. Find the arc length of the sector.

5. The arc length of a sector is 3π and the area of the sector is 27π 2

. Find the

radius and the measure of the central angle.

6. If f x( ) is a one-to-one function whose domain is all real numbers, determine f ! f −1( ) 7( ).

7. Given g x( ) = −5+ log3 x+2( ) . State the domain and range of this function.

8. Construct a graph of y = −3x 2 +9x+12 x2 − x−2

.