What is the decay factor of the exponential function represented by the table? 1/32/326

Hello mate!

this function is written in a next way:

f(x) = A(1 - r)^x

where A is the initial value, r is the decay factor.

The first thing we need to do is look at f(0)

in the table, we can see that f(0) = 6 = A(1-r)^0 = A*1

now we know that A = 6

now we got that the function is f(x) = 6(1 - r)^x

in the table, you can see that wehn x = 1, f(1) = 2, with this we can obtain the value of r.

f(1) = 6(1-r)^1 = 6(1 - r) = 2

You can use any point of the table in this step (where x is not zero, because we already used that point), i used x = 1 because the math was easier this way

6 - 6r = 2

6r = 4

r = 4/6 = 2/3

and now we know that f(x) = 6(1 - 2/3)^x

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl