Question

A gardener plants a tree and figures out that the increase in the tree's mass every year, in kilograms, is described by the equation y=40 x 1.5ˣ What was the starting mass of the tree?

a.1.5 kilograms
b. 0 kilograms
c. 40 kilograms
d. 1 kilogram

Answer 1

c. 40 kilograms

Step-by-step explanation:

The equation y=40 x 1.5ˣ tells us that the tree's mass, y, increases by 1.5 or 150% every year from the start (x = 0) to x years after the first measurement of the tree's mass, which is 40 kilograms

Answer 2

The starting mass of the tree is found by calculating the mass at year zero using the equation y = 40 × 1.5ˣ. This simplifies to 40 kilograms when x = 0.

Step-by-step explanation:

The question asks about the starting mass of a tree with yearly mass increase described by the equation y = 40 × 1.5ˣ. To find the starting mass, we look at the equation at the beginning of its growth, which is year zero (x=0). Using the exponential growth formula, we substitute x=0 into the equation:

y = 40 × 1.5^0

Since any number raised to the power of zero is 1, the equation simplifies to:

y = 40 × 1

Which further simplifies to:

y = 40

Therefore, the starting mass of the tree was 40 kilograms. Hence, the correct answer is option (c) 40 kilograms.