Question

b. the value of a phone can be represented by the equation
$v = 12,000(0.88)^t$
where $v$ is the value of the phone in dollars and $t$ is the age of the phone in years.
what is the meaning of the number 0.88 in the equation?
a. as the age of the phone increases by 1 year, the value of the phone decreases by 88%.
b. as the age of the phone increases by 1 year, the value of the phone decreases by $12.
c. as the age of the phone increases by 1 year, the value of the phone decreases by $88.
d. as the age of the phone increases by 1 year, the value of the phone decreases by 12%.

1. biologists are tracking the growth of a rabbit population. there were 45 rabbits initially at

the population is quadrupling every year.
which of the following equations can be used to find when the population of rabbits will
equal to 720?
a. $720 = (180)^x$
b. $720 = 45(4)^x$
c. $720 = 45 + 4^x$
d. $720 = 4(45)^x$

Explanation:

Question 8

Step1: Recall exponential decay formula

The general form of an exponential decay function is \( V = a(1 - r)^t \), where \( a \) is the initial value, \( r \) is the rate of decrease (as a decimal), and \( t \) is time.

Step2: Compare with given equation

The given equation is \( V = 12000(0.88)^t \). Comparing with \( V = a(1 - r)^t \), we have \( 1 - r = 0.88 \).

Step3: Solve for \( r \)

Subtract 0.88 from 1: \( r = 1 - 0.88 = 0.12 \), which is 12%. So 0.88 means the value is 88% of the previous year's value, or it decreases by 12% each year.

Step1: Recall exponential growth formula

The general form of exponential growth is \( P = P_0(b)^t \), where \( P_0 \) is the initial population, \( b \) is the growth factor, and \( t \) is time.

Step2: Identify values

Here, \( P_0 = 45 \) (initial rabbits), the population quadruples every year, so \( b = 4 \), and we want to find when \( P = 720 \). So the equation is \( 720 = 45(4)^x \) (where \( x \) is the number of years).

Answer:

D. As the age of the phone increases by 1 year, the value of the phone decreases by 12%.

Question 9