The quotient rule for exponents states that if we divide exponents with the same base, then we can subtract the exponents and keep the base unchanged.

3 0

3 years ago

Mohamed decided to track the number of leaves on the tree in his backyard each year The first year there were 500 leaves Each ye

svetlana [45]

Answer:

The required recursive formula is

$f(n)= 500\times(1.4)^{n-1}\\$

Step-by-step explanation:

Mohamed decided to track the number of leaves on the tree in his backyard each year.

The first year there were 500 leaves

$Year \: 1 = 500$

Each year thereafter the number of leaves was 40% more than the year before so that means

$Year \: 2 = 500(1+0.40) = 500\times 1.4\\$

For the third year the number of leaves increase 40% than the year before so that means

$Year \: 3 = 500\times 1.4(1+0.40) = 500 \times 1.4^{2}\\$

Similarly for fourth year,

$Year \: 4 = 500\times 1.4^{2}(1+0.40) = 500\times 1.4^{3}\\$

So we can clearly see the pattern here

Let f(n) be the number of leaves on the tree in Mohameds back yard in the nth year since he started tracking it then general recursive formula is

$f(n)= 500\times(1.4)^{n-1}\\$

This is the required recursive formula to find the number of leaves for the nth year.

Bonus:

Lets find out the number of leaves in the 10th year,

$f(10)= 500\times(1.4)^{10-1}\\\\f(10)= 500\times(1.4)^{9}\\\\f(10)= 500\times20.66\\\\f(10)= 10330$

So there will be 10330 leaves in the 10th year.

3 0

3 years ago

Read 2 more answers

On a survey, 6 students reported how many minutes it takes them to travel to school. Here are their responses.

g100num [7]

The mean would be 8.33

3 0

3 years ago

BE is a midsegment, Find the value of x. Please

Scrat [10]

Answer:

x10

Step-by-step explanation:

BE=1/2 * CD

x=CB/2

x=20/2

x=10

8 0

3 years ago