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1) a new truck that sells for $42,000 depreciates 11% each year. write a function that models the value of the truck. find the value of the truck after 8 years. round to the nearest dollar.

2) earl mows lawns one weekend. he earns $15 for each lawn that he mows. he spends $50 on gas and other supplies. what function equation represents earl's profit from mowing x lawns?

a)f(x)=50x-15
b)f(x)=50x+15
c)f(x)=15x-50
d)f(x)=15+50

3) find the common geometric series.
-2,-4,-8,-

Step-by-step explanation:

1) Depreciation

The formula for the value V of an asset after depreciation by an annual percentage rate is  

V = P(1 - r)ⁿ

where

P = present value

r = annual percentage rate

n = number of years

Data:

V = 40 000

r = 11 % = 0.11

n = 8 yr

Calculations:

(a) Function model

V= 40 000(1 - 0.11)ⁿ = 40 000(0.89)ⁿ

The function model is

(b) Future value

V = 40 000(0.89)ⁿ = 40 000 × 0.393 659 = $15 746

In eight years, the truck will be worth

2) Profit function

Income from 1 lawn = $15

  Income from x lawns =  15x

Less gas and supplies =         -50        

                 Net income = 15x – 50

The function is .

3) Geometric series

(a) Calculate the common ratio

a₁ = -2

a₂ = -4

a₃ = -8

a₄ = =16

The ratios of consecutive pairs are

a₄/a₃ = -16/(-8)  = 2

a₃/a₂ =   -8/(-4)  = 2

a₂/a₁ =   -4/(-2)  = 2

All adjacent pairs have the same common ratio r = 2.

(b) Write the formula for the series

The formula for the nth term of a geometric series is

aₙ = a₁rⁿ⁻¹

If a₁ = -2, the formula for the series is

aₙ = -2(2)ⁿ⁻¹ = -2ⁿ

The formula for the series is .

mgxmgzmgzzzlgxhhhx. dlulhx

0 and 5 minutes

step-by-step explanation:

given that one morning eight buses arrive late by the number of minutes given below:

0 8 2 6 9 2 0 7 8

write these in ascending order

0   0 2 6 7 8 8 9

in the afternoon two more buses arrive at the bus stop say by x and y minutes late.

total number of buses = 10

median = average of 4th and 5th after arranging in ascending order

since 4th entry is 6, the values of x and y should be below 6

also given 0 is the mode so either x or y or both should be 0 because then only 0 gets the maximum frequency and hence mode

thus we have

0 0 0 2 6 7 8 8 9 and another unknown entry which is below 6.

since median is 3.5, we have the unknown entry to be 5 only because then only median =( 2+5)/2

thus the after noon buses were late by 0 and 5 minutes.