Warm Up Section 3.7B

(1). Simplify: (3x-2y4)(4x-3y-4)

(2). If f(x) = 3x + 7 and g(x) = x2 – 4, finda. (f + g)(x) b. (f – g)(x) c. f(g(x))

(3). If h(x) = 7x + 2, find h-1(x).

(4). Write an expression for the 17th term of a geometric sequence in which a1 = 4 and r = -5

(5). Identify the domain and range of y = 6x – 3

Answers to Warm Up Section 3.7B

(1). (3x-2y4)(4x-3y-4) = 12x-5y0 =

(2a). (f + g)(x) = x2 + 3x + 3 (2b). (f – g)(x) = -x2 +3x + 11 (2c). f(g(x)) = 3x2 – 5

(3). h-1(x) = (x – 2)/7 (4). a17 = 4(-5)16

(5). y = 6x – 3 Domain: (-∞ , ∞)Range: y > -3

12 x5

Application of Exponential Functions

Section 3.7B

Standard: MM2A2

Essential Question: How do I apply exponential functions to real world situations?

1. The formula C = 2πr gives the circumference of a circle of radius, r. Write the inverse function, and use it to find the radius of a circle whose circumference is 14 inches.

C = 2r

Inverse: divide by 2

Let C = 14: so

rC

2

r2

14 r7

The radius is approximately 2.23 inches.

2. An infectious virus is defined by its infectivity, or how contagious the virus is to humans. The number of people (in thousands) expected to contract the virus within 6 months is modeled by y = 1.04(8.35)x where x is the infectivity rating of the virus. If the infectivity rating is 2.5, how many people would you expect to be infected within 6 months?

y = 1.04(8.35)2.5

y ≈ 209.532 (thousand)

In 6 months 209,532 people will be infected.

3. Compound interest is interest paid on the initial investment, called the principal and on previously earned interest. Consider an initial investment (principal) deposited in an account that pays interest at an annual rate, (expressed as a decimal), compounded times per year. The amount in the account after years is given by the equation

You deposit $3500 in an account that earns 2.5% annual interest. Find the balance after one year if the interest is compounded with the given frequency: a. annually b. quarterly c. monthly

1nt

rA P

n

(3a). 11

1

025.013500

A 50.3587A

(3b). 14

4

025.013500

A 32.3588A

(3c). 112

12

025.013500

A 51.3588A

4. A Petri dish contains 3 amoebas. An amoeba is a microorganism that reproduces using the process of fission, by simply dividing itself into two smaller amoebas. Once the new amoebas mature, they will go through the same process.

a. Write the terms of the sequence describing the first four generations of the amoeba in the Petri dish.

1 2 3 43 6 12 24

4. A Petri dish contains 3 amoebas. An amoeba is a microorganism that reproduces using the process of fission, by simply dividing itself into two smaller amoebas. Once the new amoebas mature, they will go through the same process.

b. Write a rule for the nth term of the sequence. c. Find the 10th term of the sequence and describe in words what this term represents.

an = 3(2)n -1

a10 = 3(2)9

a10 = 1536

The 10th generation will have are 1,536 amoebas if none die!

5. You invest $5000 in a retirement plan. The plan is expected to have an annual rate of return of 8%. Write an exponential model for the amount of money in the plan after years. What is the balance of the account after 25 years? How much would you have after 25 years if the initial investment had been $10,000?

y = 5000(1 + 0.08)t

y = 5000(1.08)25 = 34,242.38

y = 10000(1.08)25= 68,484.75

6. You have a coupon for $200 off the price of a personal computer. When you arrive at the store, you find that the computers are on sale for 20% off. Let x represent the original price of the computer.

a. Use function notation to describe your cost, f(x), using only the coupon.

b. Use function notation to describe your cost, g(x), using only the discount.

f(x) = x – 200

g(x) = 0.8x

6. You have a coupon for $200 off the price of a personal computer. When you arrive at the store, you find that the computers are on sale for 20% off. Let x represent the original price of the computer.

c. Form the composition of the functions f and g that represents your cost if you apply the coupon first, then apply the 20% discount.

g(f(x)) = g(x – 200)

= 0.8(x – 200)

= 0.8x – 160

6. You have a coupon for $200 off the price of a personal computer. When you arrive at the store, you find that the computers are on sale for 20% off. Let x represent the original price of the computer.

d. Form the composition of the functions f and g that represents your cost if you apply the discount first, then apply the coupon.

f(g(x)) = f(0.8x)

= 0.8x – 200

e. You would pay less for the computer if you appliedthe discount first.