Answer:
Explanation:
Since Mary spends the same amount of money each day, the bank account will decrease in a linear fashion, so the equation that will model Mary's spending is a straight line. Let's find an equation in the form of y=mx + B, where m is the slope and b the y-intercept (the value of y when x is zero. Let x be the amount in Mary's account, and y be the number of days Mary has been spending the same amount each day since day 0, when she started her spending habit.
Let's start with finding the slope, whcih in this case is the rate at whiich Mary is pending money, expressed as $/day. We have two know points in Mary's account history:
Day Account($)
10 56
14 48
We can use these two pints to calculate the slope, also known as the Rise/Run.
Rise: (48-56) = -8 [Negative, since the account drops each day].
Run: (14-10) = 4
Slope: Rise/Run is (-8/4) or -2. Mary spends $2/day, every day. The negative means "spends" in this scenario.
So we can write y = -2x+b
We need to find b, the y-intercept. This is the value of y (the bank account amount) that is in the account when x = 0, before any spending occurs.
To find b, use either of the two known points. Let's try (10,56) [Day 10, $56].
y = -2x+b
56 = -2*(10)+b for (10,56)
56 = -20 + b
b = 76
Mary has $76 in her account on day 0.
The equation that models Mary's bank account is y = -2x + 76. She spends $2 per day from an account that started with $76.
CHECK:
Does this equation correctly predict the known account information?
Predicted from y = -2x + $76, where y is the bank account (in $) and x is the days since spending of $2/day began
Predicted
Day Bank Account ($) Known($)
0 76
1 74
2 72
3 70
4 68
5 66
6 64
7 62
8 60
9 58
10 56 56 Match
11 54
12 52
13 50
14 48 48 Match
The equation is f(x) = -2x + 76, where x is days since spending $2/day from an account that had $76.
None of the answer options matches this expression. The closest is a) f(x) = 56-2x. But this assumes day 10 is day 0. We can try it:
Does f(x) = 56-2x predict a bank balance of $48 on day 14?
f(x) = 56-2x
f(14) = 56-2*(14) for x = 14
f(14) = 56-28
f(14) = $28 No. This equation does NOT predict the correct amount on Day 14.
The correct expression is f(x) = -$2x + $76