How to Solve for x. -1/2 (x + 2) + 1 1/2 x = 3

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

Three people invest in a treasure dive, each investing the amount listed below. The dive results in 40 gold coins. Apportion tho

garri49 [273]

Answer:

Alice: 20 coins, Ben: 16 coins, and Carlos: 4 coins.

Step-by-step explanation:

We know that the dive results in 40 gold coins.

We know that:

Alice: $7,600 Ben: $5,900 Carlos: $1,400.

So they have $ 14900 in total.

Now we will divide that money by 40.

$x=\frac{14900}{40}\\\\x=372.5$

So 1 gold coin costs $ 372.5. Now we will calculate how much they can get for the money they have.

$A=\frac{7600}{372.5}=20.4\\\\B=\frac{5900}{372.5}=15.8\\\\C=\frac{1400}{372.5}=3.75\\$

We conclude that:

Alice: 20 coins, Ben: 16 coins, and Carlos: 4 coins.

6 0

3 years ago

A=30 and AB=4 how long is bc

mojhsa [17]

Answer:

bc is 26

Step-by-step explanation:

7 0

3 years ago

Is 2,6 a solution to x+y=8 and 3x-y=0

algol13

Answer:

Yes.

Step-by-step explanation:

x=2

y=6

(2) + (6) = 8

8 = 8

3(2) - (6) = 0

6 - 6 = 0

0 = 0

7 0

3 years ago

Annual sales for a small boutique were $863,000in 2010. Since then the sales have increased at a rate of 2.5% per year. Find the

Alborosie

Answer:

1,035,600

Step-by-step explanation:

since the rate sales increased 2.5% per year 8*2.5=20/100=0.2*863,000=172,600 and since we already are earning 863,000 so 863,000+172,600=1,035,600

3 0

2 years ago

How to Solve for x. -1/2 (x + 2) + 1 1/2 x = 3 ​

How to Solve for x. -1/2 (x + 2) + 1 1/2 x = 3