1. "The limit on John's credit card is defined by the function f(x)=15,000+1.5x," indicating that if John's monthly income is $5,000, he can spend a maximum of f(5,000)=15,000+1.5*5,000=15,000+ 7,500=22,500 (dollars). As another example, if John's monthly income is $8,000, then he can spend up to f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars). 2. If we consider the maximum amount John can spend as y, it can be represented as y=15,000+1.5x. To express x, the monthly income, in terms of y, we rearrange this equation: y=15,000+1.5x results in 1.5x = y-15,000. Therefore, in functional notation, x is a function, referred to as g, based upon y, the maximum sum. Generally, we denote the variable of a function by x, so we redefine g as: This tells us that if the maximum amount that John can spend is $50,000, then his monthly income would be $23,333. 3. If John's limit is $60,000, his monthly income equals $30,000. Note: g is deemed as the inverse function of f because it reverses the actions of f.
Given data:
a₃ = 9/16
aₓ = -3/4 · aₓ₋₁
Here, x represents the number of terms ('x' can also be referred to as 'n')
To determine the 7th term (a₇):
We know that aₓ = -3/4 · aₓ₋₁
Thus,[ [TAG_10]]a₃ = -3/4 · a₃₋₁
a₃ = -3/4 · a₂
9/16 = -3/4 · a₂
a₂ = 9/16 × -4/3
a₂ = -36/48
a₂ = -3/4
Next,[ [TAG_20]]aₓ = -3/4 · aₓ₋₁
a₄ = -3/4 · a₄₋₁
a₄ = -3/4 · a₃
a₄ = -3/4 · 9/16
a₄ = -27/64
a₄ = -27/64
For a₅,[ [TAG_30]]aₓ = -3/4 · aₓ₋₁
a₅ = -3/4 · a₅₋₁
a₅ = -3/4 · a₄
a₅ = -3/4 × -27/64
a₅ = 81/256
For a₆,[ [TAG_39]]aₓ = -3/4 · aₓ₋₁
a₆ = -3/4 · a₆₋₁
a₆ = -3/4 · a₅
a₆ = -3/4 × 81/256
a₆ = -243/1024
Finally, for a₇,[ [TAG_48]]aₓ = -3/4 · aₓ₋₁
a₇ = -3/4 · a₇₋₁
a₇ = -3/4 · a₆
a₇ = -3/4 × -243/1024
a₇ = 729/4096
Answer:
Step-by-step explanation:
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This scenario is similar to a compound interest problem where the following formula is utilized:
Here:
C is the principal amount
j stands for the interest rate
n represents the number of periods
M is the total amount
By applying this formula to our issue, we establish:
C equals the initial population
j indicates the annual growth rate
n corresponds to the years elapsed
M signifies the final population
Let's proceed with the calculations...
C = 14000
j = 3% = 3/100 = 0.03
n = 6
M =?
Substituting the known values and calculating gives us:
M = C. 
M = 14000. 
M = 14000. 
M = 14000. 1.19
M = 16,716.7
Thus, the result is 16,717
:-)
