Which is the graph of the sequence defined by the function f(x+1)=2/3f(x) if the initial value of the sequence is 108

First four terms of this sequence are:

.

This sequence is decreasing and seems to be exponential. See whether you can determine such a and b, that :

1.

, then a=108,

2.

, then .

3. Check for x=2 and x=3:

a) x=2:

(true),

b) x=3:

(true).

4. Check for all x:

.

Equate f(x+1) and 2/3f(x):

is true equality for all x.

the graph is the graph of the function .

See picture attached.

Step-by-step explanation:

For x = 1, f(x) = 108. For the next x-value which is 2, that is, x+1, f(x+1) = (2/3)*f(x) = (2/3)*108 = 72.   For the next x-value, which is 3, f(x+1) = (2/3)*f(x) = (2/3)*72 = 48 . For the next x-value, which is 4, f(x+1) = (2/3)*f(x) = (2/3)*48 = 32 . And so on.

xf(x)

1108

272

348

432

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.