Question

1. four aerial photographers will need 6 batteries to operate their drones. each found a different website that sells rechargeable batteries.

website a
website b
website c
batteries
1
2
3
5
6
cost ($)
39.10
41.20
43.30
47.50
49.60
website d
$y = 3.5x + 28$
a. for each website, find the cost of 6 rechargeable batteries and a charger. which website has the best price?
website a charges ______ for 6 batteries & a charger.
website b charges ______ for 6 batteries & a charger.
website c charges ______ for 6 batteries & a charger.
website d charges ______ for 6 batteries & a charger.
website ______ has the best price.
b. the fixed value represents ______
the rate of change represents ______
c. determine the cost of the charger from website a.
______
determine the cost of the charger from website c.
______
determine the cost of the charger from website d.
______

Explanation:

Step1: Calculate Website A total cost

First, find the cost per battery from the graph: when $x=0$, $y=40$ (fixed cost/charger), rate of change is $\frac{52-40}{8}=1.5$. Total cost for 6 batteries: $y=1.5(6)+40=9+40=49$

Step2: Calculate Website B total cost

Cost of 6 batteries: $6\times2.30=13.80$. Add charger cost: $13.80+35=48.80$

Step3: Calculate Website C total cost

Use the table: cost for 6 batteries is $\$49.60$ (includes charger)

Step4: Calculate Website D total cost

Substitute $x=6$ into $y=3.5x+28$: $y=3.5(6)+28=21+28=49$

Step5: Compare total costs

Compare $49$, $48.80$, $49.60$, $49$

Step6: Find Website A charger cost

From graph, $x=0$ gives $y=40$

Step7: Find Website C charger cost

Subtract 1 battery cost from total: $39.10-3.20=35.90$ (rate of change is $41.20-39.10=2.10$, verify: $39.10-2.10=37$? Correct: $37+2.10(1)=39.10$)

Step8: Find Website D charger cost

From $y=3.5x+28$, fixed term is 28

Step9: Define fixed/rate of change

Fixed value = charger cost, rate = per-battery cost

Answer:

Part A:

Website A charges $\boldsymbol{\$49}$ for 6 batteries & a charger.
Website B charges $\boldsymbol{\$48.80}$ for 6 batteries & a charger.
Website C charges $\boldsymbol{\$49.60}$ for 6 batteries & a charger.
Website D charges $\boldsymbol{\$49}$ for 6 batteries & a charger.
$\boldsymbol{\text{Website B}}$ has the best price.

Part B:

The fixed value represents $\boldsymbol{\text{the cost of the charger}}$
The rate of change represents $\boldsymbol{\text{the cost per battery}}$

Part C:

Determine the cost of the charger from Website A: $\boldsymbol{\$40}$
Determine the cost of the charger from Website C: $\boldsymbol{\$37}$
Determine the cost of the charger from Website D: $\boldsymbol{\$28}$