Answer:
Step-by-step explanation:
Part A
If the gardener increases the number of dahlia plants by buying the new bulbs,
Let the equation representing year (x) and number of bulbs purchased (y) is,
y = mx + b
Here, m = Number of plants purchased each year
b = Initial numbers of plants
For x = 0, and y = 6,
6 = m(0) + b
b = 6
For x = 1, y = 56,
56 = m(1) + 6
m = 50
Therefore, equation for this method of increasing the numbers of plants will be,
y = 50x+ 6
Let the equation for the second method of increasing the number of plants is represented by the equation,
y = a(b)ˣ
From the data given in the table,
For x = 0, y = 6
6 = a(b)⁰
a = 6
For x = 1, y = 12
12 = 6(b)¹
b = 2
Therefore, equation representing the second method (By diving the existing bulbs) will be,
y = 6(2)ˣ
Part B
By substituting the value of x = 10 years,
Method - 1
y = 50(10) + 6
y = 506 plants
Method - 2
y = 6(2)¹⁰
y = 6144 plants
Part C
After 5 years number of plants by method - 1,
y = 50(5) + 6
= 256
After 5 years number of plants by method - 2,
y = 6(2)⁵
y = 192
Similarly, After 10 years number of plants by method - 1,
y = 50(10) + 6
= 506
By method - 2,
y = 6(2)¹⁰
y = 6144
Since, number of plants after 5 years are less by the second method as compared to method 1
But after 10 years second method results the number of plants more than method-1,
Therefore, gardener should adopt method 2 for increasing the numbers of plants.
