Answer : y>0
f(x) = 9*2^x
f(x) is an exponential function

When we plug in positive value for x , the value of y is positive
When we plug in negative value for x , the value y is also positive
So for any value of x, the y value is positive always.
Range is the set of y values for which the function is defined
y values are positive , so range is y >0
Answer:
We are known that Katya and her friends stand in a circle and both neighbors are of same gender this means that the person on the right and the person on the left of anyone in the circle will be of same gender either a girl or a boy.
We are given that there are five boys, we could have considered the circle to be only composed of boys but we are given there is a girl Katya within it and it is also mentioned that 'Katya and her friends' that means there can be more girls in the circle.
Now when we draw a circle on a page and mark points K for Katya and boys B1 and B2 on right and on the left of Katya we will get to know that after each boy there has to be a space vacant because on that space a girl should be positioned only then we will meet the criteria of both gender's same on the neighbor side of each person.
Also we will mark boys B1,B2,B3,B4,B5 as five boys and leave space vacant for girls and with those vacant spaces we get to know there will be 4 vacant spaces and one is Katya herself.
Therefore there will be a total of five girls in the circle one is Katya and other four.
Given data :
a₃ = 9/16
aₓ = -3/4 · aₓ₋₁
Where x is the number of terms ('x' is also written as 'n')
To find the 7th term (a₇):
We know that aₓ = -3/4 · aₓ₋₁
So,
a₃ = -3/4 · a₃₋₁
a₃ = -3/4 · a₂
9/16 = -3/4 · a₂
a₂ = 9/16 × -4/3
a₂ = -36/48
a₂ = -3/4
Again,
aₓ = -3/4 · aₓ₋₁
a₄ = -3/4 · a₄₋₁
a₄ = -3/4 · a₃
a₄ = -3/4 · 9/16
a₄ = -27/64
a₄ = -27/64
For a₅,
aₓ = -3/4 · aₓ₋₁
a₅ = -3/4 · a₅₋₁
a₅ = -3/4 · a₄
a₅ = -3/4 × -27/64
a₅ = 81/256
For a₆,
aₓ = -3/4 · aₓ₋₁
a₆ = -3/4 · a₆₋₁
a₆ = -3/4 · a₅
a₆ = -3/4 × 81/256
a₆ = -243/1024
For a₇,
aₓ = -3/4 · aₓ₋₁
a₇ = -3/4 · a₇₋₁
a₇ = -3/4 · a₆
a₇ = -3/4 × -243/1024
a₇ = 729/4096
We have been given an equation
. We are asked to solve the equation for t.
First of all, we will divide both sides of equation by a.


Now we will take natural log on both sides.

Using natural log property
, we will get:

We know that
, so we will get:


Now we will divide both sides by c as:


Therefore, our solution would be
.
There is multiple ways but one of them is 3 SUV and 1 car and that will give him $315.
I hope this helps :)