Atree 7ft tall grows an average pf 6in each year. which equation models the trees height h after x years?

a)h=0.5x+7
b)h=+-6x+7
c)h=-0.5x+7
d)h=6x +7

A)  h=0.5x+7

Step-by-step explanation:

given

initial height = 7 feet

growth rate = 6 in = 0.5 feet / year

let # of growing years = x

For a linear growth rate:

height after x years, h = initial height + (# of growing years) * (growth rate)

substiuting the values above into this equation

h = 7 feet + (x years) * (0.5 feet/year)

or

h = 7 + 0.5x (rearranging)

h = 0.5x + 7

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

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step-by-step explanation:

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