Question

A daylily farm sells a portion of their daylilies and allows a portion to grow and divide. The recursive formula an=1.5(an-1)-100 represents the number of daylilies, a, after n years. After the fifth year, the farmers estimate they have 2225 daylilies. How many daylilies were on the farm after the first year?

Answer 1

Answer:

c. 600

Step-by-step explanation:

Answer 2

Answer:

600 daylilies were on the farm after the first year.

Step-by-step explanation:

Given : A daylily farm sells a portion of their daylilies and allows a portion to grow and divide. The recursive formula $a_n=1.5(a_{n-1})-100$ represents the number of daylilies, a, after n years. After the fifth year, the farmers estimate they have 2225 daylilies.

To find : How many daylilies were on the farm after the first year?

Solution :

The recursive formula is  $a_n=1.5(a_{n-1})-100$

We have given after the fifth years number of daylilies, $a_5=2225$

Put n=5 in the formula we get,

$a_5=1.5(a_{5-1})-100$

$2225=1.5(a_{4})-100$

$2325=1.5(a_{4})$

$\frac{2325}{1.5}=a_4$

$a_4=1550$

Now, put n=4 in the formula,

$a_4=1.5(a_{4-1})-100$

$1550=1.5(a_{3})-100$

$1650=1.5(a_{3})$

$\frac{1650}{1.5}=a_3$

$a_3=1100$

Now, put n=3 in the formula,

$a_3=1.5(a_{3-1})-100$

$1100=1.5(a_{2})-100$

$1200=1.5(a_{2})$

$\frac{1200}{1.5}=a_2$

$a_2=800$

Now, put n=2 in the formula,

$a_2=1.5(a_{2-1})-100$

$800=1.5(a_{1})-100$

$900=1.5(a_{1})$

$\frac{900}{1.5}=a_1$

$a_1=600$

Which means after first year is $a_1=600$

Therefore, 600 daylilies were on the farm after the first year.