Mohamed decided to track the number of leaves on the tree in his backyard each year. the first year, there were 500 leaves. each year thereafter, the number of leaves was 40% more than the year before. let f(n) be the number of leaves on the tree in Mohamed's backyard in the n^th year since he started tracking it. f is a sequence. what kind of sequence is it?
Number of leaves on the tree in first year = 500
The number of leaves was 40% more than the year before.
So rate of increase is 40/100 = 0.4
We use exponential growth formula,
f(n) = a(1+r)^n
Where a is the initial number, r is the rate of growth, n is the number of years
We know a= 500, r= 0.4
f(n) = 500(1+0.4)^n
f(n) = 500(1.4)^n
Plug in n=1,2,3...
f(1) = 500
f(2) = 500 * 1.4^1
f(3) = 500 * 1.4^2 and so on
From this we can see that the common ratio is 1.4
Hence it is a Geometric sequence.
Answer:
(x + 7)2 + (y + 1)2 = r2.
To get we use point (8, 7): (8 + 7)2 + (7 + 1)2 = r2, r2 = 225 + 64 = 289 = 172.
So, equation of circle: (x + 7)2 + (y + 1)2 = 289
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
3^1=3 divided by 8 will give a remainder of 3
3^2=9 divided by 8 will give a remainder of 1
3^3=27 divided by 8 will give a remainder of 3
3^4=81 divided by 8 will give a remainder of 1
3^5=243 divided by 8 will give a remainder of 3
You will notice that 3^n will give 3 when n is odd number and 1 when n is even number
Since n=99 and 99 is an odd number,
Then the remainder is 3
Answer: Our required equation would be
Step-by-step explanation:
Since we have given that
y=30, when x = 6.
As there is direct proportion between x and y.
so, it becomes,
So, the equation connecting y and x would be
When we put the value of k, we get that
Hence, our required equation would be y=5x