How do I find the rate of decline?

Question

In 2006 the number is 127.5 and in 2100 it is 64 how do I find the annual rate of decline?

Answer 1

127.5 - 64 = 63.5
2006 - 2100 = -94
Assuming the number and the year have a linear relationship, then
63.5/-94 = -.675531914894

Answer 2

You need to know whether it is a linear rate of decline or exponential (such as the natural log). If it is linear, then the answer is just (127.5 - 64)/(2100 - 2006), which equals 63.5/94 = 0.675532 (somethings) per year. If it is an exponential decay, more information needs to be given.

Answer 3

This is an equataion of 94 powers.
127.5*((1-x)^94)=64
You do the rest of the math. I quit.

Answer 4

T1= 2006
T2=2100
Total length of time for declination (T)=2100-2006
=94

Original value (P)=127.5
Final value (A)=64
Let, rate of declination be D

For rate of declination, we know that:

A=P(1-D/100)^T

Putting our given values, we have:

64=127.5(1-D/100)^94
64/127.5=(1-D/100)^94

simplying LHS, we have:

128/255=(1-D/100)^94
now,

(1.052972738)^94=128; and:
(1.060721792)^94=255

Therefore, we have:

(1.052972738/1.060721792)^94=(1-D/100)^94

Hence, we deduce,

1.052972738/1.060721792=1-D/100
Solving for D, we have:

D=0.73.

Hence, your actual rate of declination is 0.73%

Answer 5

64 = 127.5 * (1+x)^94
ln(64) = ln(127.5) + 94 * ln(1+x)
ln(1+x) = ln(64/127.5) / 94
1+x = exp(ln(64/127.5)/94)
x = exp(ln(64/127.5)/94) -1
x = -0.007305453
decline rate = 0.73%

Answer 6

I bet you are in beginning algebra so yo just need to find the slope of the line that goes through the point (2006,127.5) and (2100,64)

Answer 7

Try Google.

Answer 8

look at a graph