Mara planted tulips in her garden. In the first year, the garden produced 6 bulbs. In the second year, it produced 18 bulbs, and in the third year it produced 54 bulbs. If this pattern continues, how many bulbs should Mara expect in the fifth year?
To find the pattern, we can use exponents. Each year, the number of bulbs Mara gets is 3 times the number from the previous year. We can write this as:
Year 1: 6 = 3^1 x 2
Year 2: 18 = 3^2 x 2
Year 3: 54 = 3^3 x 2
So the pattern is: Number of bulbs = 3^year x 2
Using this pattern, we can find the number of bulbs in the fifth year:
Number of bulbs in year 4 = 3^4 x 2 = 81 x 2 = 162
Number of bulbs in year 5 = 3^5 x 2 = 243 x 2 = 486
Therefore, Mara should expect 486 bulbs in the fifth year.
To determine the pattern in bulb production, we can observe that each year the number of bulbs is multiplied by 3.
In the first year: 6 bulbs
In the second year: 6 bulbs * 3 = 18 bulbs
In the third year: 18 bulbs * 3 = 54 bulbs
To find out how many bulbs Mara should expect in the fifth year, we need to multiply the number of bulbs in the third year by 3 again.
In the fourth year: 54 bulbs * 3 = 162 bulbs
In the fifth year: 162 bulbs * 3 = 486 bulbs
Therefore, Mara should expect 486 bulbs in the fifth year.