Question

Theresa's Trees is a tree-planting company hired by various local governments, who pay $2 per tree planted. The number of trees they can plant per day is given by Q = 16K^α.

a. Calculate the value of α if Theresa's Trees can plant 64 trees per day when K = 2.

Answer 1

To find the value of α when Theresa's Trees can plant 64 trees per day with K = 2, we use the formula Q = 16K¹⁴ and solve for α. The calculation reveals that α equals 2.

Step-by-step explanation:

We have been given that Theresa's Trees, a tree-planting company, can plant a number of trees per day given by the equation Q = 16K¹⁴. The company gets pay from local governments at a rate of $2 per tree planted. To calculate the value of α, we can use the information provided that when K = 2, the number of trees planted per day, Q, is 64.

The equation with the given values is 64 = 16(2)¹⁴. To solve for α, we first simplify the equation:

64 = 16(2¹⁴)

64 = 16 * 2¹⁴

64 = 16 * (2¹⁴)

4 = 2¹⁴ (Dividing both sides by 16)

Now, we recognize that 2² = 4, so:

4 = 2²

2¹⁴ = 2²

α = 2 (Since the bases are the same, the exponents must be equal)

Therefore, the value of α is 2.