Answer:
Step-by-step explanation:
Each successive year, he
earned a 5% raise. It means that the salary is increasing in geometric progression. The formula for determining the nth term of a geometric progression is expressed as
Tn = ar^(n - 1)
Where
a represents the first term of the sequence(amount earned in the first year).
r represents the common ratio.
n represents the number of terms(years).
From the information given,
a = $32,000
r = 1 + 5/100 = 1.05
n = 20 years
The amount earned in his 20th year, T20 is
T20 = 32000 × 1.05^(20 - 1)
T20 = 32000 × 1.05^(19)
T20 = $80862.4
To determine the his total
earnings over the 20-year period, we would apply the formula for determining the sum of n terms, Sn of a geometric sequence which is expressed as
Sn = (ar^n - 1)/(r - 1)
Therefore, the sum of the first 20 terms, S20 is
S20 = (32000 × 1.05^(20) - 1)/1.05 - 1
S20 = (32000 × 1.653)/0.05
S20 = $1057920
-1.9 = x/.5 given equation
multiply both sides by .5
.5(-1.9) = x/(.5) *(.5)
-.95 = x
check: -1.9 = -.95/ .5
Answer:
y = -1/3x - 5
Step-by-step explanation:
Use rise over run to find the slope: (y2 - y1) / (x2 - x1)
Plug in the points:
(y2 - y1) / (x2 - x1)
(-7 + 3) / (6 + 6)
-4 / 12
= -1/3
Plug in the slope and a point into y = mx + b, and solve for b:
y = mx + b
-3 = -1/3(-6) + b
-3 = 2 + b
-5 = b
Plug in the slope and b into y = mx + b
y = -1/3x - 5 is the equation of the line
<span>nth term = 7n - 3
n = 1,2,3,4....</span>
