Question

1. mr. bean’s custom scooter is worth $500, but is increasing in value v by 4% every year t.

a. exponential growth
b. exponential decay
c. linear growth
d. linear decay
function: _______________

1. mr. bean’s scooter just got new tires that have a tread depth d of 0.3 inches and decays at a rate of 2.8% per month m.

a. exponential growth
b. exponential decay
c. linear growth
d. linear decay
function: _______________

1. you have $100 in savings s but are paying for a phone that costs $20 per month m.

a. exponential growth
b. exponential decay
c. linear growth
d. linear decay
function: _______________

1. you purchase a baseball card for $50. the value v of the card increases by $1.50 per year t.

a. exponential growth
b. exponential decay
c. linear growth
d. linear decay
function: _______________

1. use x and f(x) for your variables.

a. exponential growth
b. exponential decay
c. linear growth
d. linear decay
function: _______________
(0, 3)
(1, 1.2)

1. use x and f(x) for your variables.

a. exponential growth
b. exponential decay
c. linear growth
d. linear decay
function: _______________
(0, 3)
(1, 6)

Explanation:

Question 17

Step1: Identify Growth/Decay Type

The scooter's value increases by 4% yearly, so it's exponential growth (a).

Step2: Formulate Exponential Function

Initial value \( P = 500 \), rate \( r = 0.04 \), time \( t \). Formula: \( y = P(1 + r)^t \). Substitute: \( y = 500(1 + 0.04)^t = 500(1.04)^t \).

Step1: Identify Growth/Decay Type

Tire tread depth decays (decreases) at 2.8% monthly, so exponential decay (b).

Step2: Formulate Exponential Function

Initial depth \( P = 0.3 \), rate \( r = 0.028 \), time \( m \). Formula: \( d = P(1 - r)^m \). Substitute: \( d = 0.3(1 - 0.028)^m = 0.3(0.972)^m \).

Step1: Identify Growth/Decay Type

Savings decrease by $20 monthly (constant rate), so linear decay (d).

Step2: Formulate Linear Function

Initial savings \( s_0 = 100 \), rate \( -20 \) per month \( m \). Formula: \( s = 100 - 20m \).

Answer:

a. Exponential Growth
Function: \( y = 500(1.04)^t \)

Question 18