Hey mate. Here is your Answer:
f(x) = 50 + 25(x - 1)
Step-by-step explanation:
Let's write an equation to represent the function that will allow Damon to calculate the cost of his video game membership service:
Lifetime membership fee = $ 50
First video game is free
Then any video game purchased after = $ 25.
Let x to represent the total cost of the video game membership service, in consequence we can write the equation this way:
f(x) = 50 + 25(x - 1)
If x = 1, then f(1) = 50 + 0 = 50
If x = 2, then f(2) = 50 + 25 = 75
If x = 5, then f(5) = 50 + 100 = 150
<h3>
Answer: Choice A. P = 1000M</h3>
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Explanation:
Use the log rule
log(A/B) = log(A) - log(B)
this works for any valid log base
So we can say
- log(P/N) = log(P) - log(N)
- log(M/N) = log(M) - log(N)
meaning that
- log(P/N) = 8 turns into log(P) - log(N) = 8
- log(M/N) = 5 turns into log(M) - log(N) = 5
We have this system of equations
Subtract the equations straight down. You'll find the log(N) terms cancel out and we have the new equation log(P) - log(M) = 3 which transforms into log(P/M) = 3
Lastly, convert the log equation into its exponential equivalent form using the idea that log(b,x) = y turns into y = b^x, where b is the base
Throughout this problem, the base wasn't given. Instead its implied we're talking about base 10.
So,
log(P/M) = 3
P/M = 10^3
P/M = 1000
P = 1000M
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Alternatively,
log(P/N) = 8 turns into P/N = 10^8
log(M/N) = 5 turns into M/N = 10^5
meaning that we can divide the two equations to get P/M = (10^8)/(10^5). That simplifies to P/M = 1000 and rearranges to P = 1000M
( x-5)/-2=(x-1)/-3
Cross multiply
-3(x-5)=-2(x-1)
Distribute
-3x +15 = -2x +2
Add 2x to both sides
-x +15 = 2
Subtract 15 from both sides
-x = -13
x=13