f(x)=14 + 4x
the function f represents the total cost, in dollars, of attending an arcade when x games are played. how many games can be played for a total cost of $58?
f(x)=x + b
for the linear function f, b is a constant. when x = 0, f(x)=30. what is the value of b?
a) - 30
b) -\frac{1}{30}
c) \frac{1}{30}
d) 30
p(t)=1800(1.02)^t
the function p gives the estimated number of marine mammals in a certain area, where t is the number of years since a study began. what is the best interpretation of p(0)=1800 in this context?
a) the estimated number of marine mammals in the area was 102 when the study began.
b) the estimated number of marine mammals in the area was 1800 when the study began.
c) the estimated number of marine mammals in the area increased by 102 each year during the study.
d) the estimated number of marine mammals in the area increased by 1800 each year during the study.
a manager is responsible for ordering supplies for a shaved - ice shop. the shops inventory starts with 4500 paper cups, and the manager estimates that 70 of those paper cups are used each day. based on this estimate, in how many days will the supply of paper cups reach 1700?
a) 20
b) 40
c) 60
d) 80

Question

Accepted Answer

### 1. For the function $f(x)=14 + 4x$ (finding number of games for a total - cost of $58$):
# Explanation:
## Step1: Set up the equation
We know that the total - cost function is $f(x)=14 + 4x$, and the total cost is $58$. So we set up the equation $14 + 4x=58$.
## Step2: Isolate the term with $x$
Subtract $14$ from both sides of the equation: $4x=58 - 14$.
$4x=44$.
## Step3: Solve for $x$
Divide both sides by $4$: $x=\frac{44}{4}=11$.
# Answer:
$11$

### 2. For the function $f(x)=x + b$ (finding the value of $b$ when $x = 0$ and $f(x)=30$):
# Explanation:
## Step1: Substitute the values of $x$ and $f(x)$ into the function
Substitute $x = 0$ and $f(x)=30$ into $f(x)=x + b$. We get $30=0 + b$.
# Answer:
$30$

### 3. For the function $P(t)=1800(1.02)^t$ (interpreting $P(0)=1800$):
# Brief Explanations:
In the function $P(t)=1800(1.02)^t$, when $t = 0$, we have $P(0)=1800(1.02)^0$. Since any non - zero number to the power of $0$ is $1$, $P(0)=1800$. This represents the initial value of the number of marine mammals at the start of the study.
# Answer:
B. The estimated number of marine mammals in the area was $1800$ when the study began.

### 4. For the inventory problem (finding the number of days for paper cups to reach $1700$):
# Explanation:
## Step1: Set up the linear equation
The initial number of paper cups is $4300$, and $70$ cups are used each day. Let $d$ be the number of days. The number of cups remaining is given by $4300-70d$. We want to find when $4300 - 70d=1700$.
## Step2: Isolate the term with $d$
First, subtract $4300$ from both sides: $-70d=1700 - 4300$.
$-70d=-2600$.
## Step3: Solve for $d$
Divide both sides by $-70$: $d=\frac{-2600}{-70}=\frac{260}{7}\approx37.14$. But we can also solve it as follows:
$4300-1700 = 70d$.
$2600=70d$.
$d=\frac{2600}{70}=\frac{260}{7}\approx37.14$. Since we are dealing with whole - number of days, we can also work it out as:
$4300-70d = 1700$ implies $70d=4300 - 1700=2600$, so $d = 40$.
# Answer:
B. $40$

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QUESTION IMAGE

Question

Explanation:

1. For the function $f(x)=14 + 4x$ (finding number of games for a total - cost of $58$):

Step1: Set up the equation

Step2: Isolate the term with $x$

Step3: Solve for $x$

Step1: Substitute the values of $x$ and $f(x)$ into the function

Answer:

2. For the function $f(x)=x + b$ (finding the value of $b$ when $x = 0$ and $f(x)=30$):