Answer:
B. y = x + 3
Step-by-step explanation:
Let m represent the slope of the line.
Let c represent the y-intercept of the line.
Then the equation of the line with slope m and y-intercept c is given by ![\[y=mx+c\] ](https://tex.z-dn.net/?f=%5C%5By%3Dmx%2Bc%5C%5D%0A)
In this case, the value of m is 1 and the value of c is 3.
Substituting the given values in the equation:
![\[y=x+3\] ](https://tex.z-dn.net/?f=%5C%5By%3Dx%2B3%5C%5D%0A)
Among the given options, option B represents the correct equation of the line.
A) New branch in:
2nd stage=2
3rd stage=4
4th stage=8
which can be listed as 2,4,8,...
Here,
2nd term/1st term=4/2=2
3rd term/2nd term=8/4=2
Since common ratio is 2, the given sequence is geometric sequence.
b) The required function is,
B(n)=2^(n-1)
{just put n=1,2,3.. here to check if it gives accurate no of branches in each step or not}
where n is stage number
c)Using above function to calculate total no of branches growing out in the 8th stage,
B(8)=2^(8-1)=2^7=128
Lets calculate linear equation
assume
y = f(x)= mx +b
now given
f(0) = 2
m×0+b = 2
b = 2
so b = 2
given f(4) = 0.125 = 1/8
m×4 + 2 = 1/8
4m = 1/8-2= -15/8
m = -15 /(8×4) = -15/32
so linear equation is
y = mx + b = -15x/32 + 2
exponential equation is same as you have written
y = 2(0.5)^x
now put values of x in each equation to get value of y
x =0
linear y = -15×0/32+2 = 2
exp y = 2(0.5)^0 = 2×1 = 2
x =1
linear y = -15×1/32+2 = 2-15/32= 49/32
exp y = 2(0.5)^1 = 2×1/2 = 1
x =2
linear y = -15×2/32+2 = 2-30/32= 17/16
exp y = 2(0.5)^2 = 2×1/4 = 0.5
x =3
linear y = -15×3/32+2 = 2-45/32= 19/32
exp y = 2(0.5)^3 = 2×1/8= 0.25
x =4
linear y = -15×4/32+2 = 2-60/32= 4/32 = 0.125
exp y = 2(0.5)^4= 2×1/16 = 1/8= 0.125
f(x)= mx+b is your answer
I think its 4.8 miles, dont hold me to that though
