To determine the starting mass of the tree, we need to understand what the term "starting mass" means in the context of the given equation. The equation provided is [tex]\( y = 40 \cdot 1.5^x \)[/tex], where [tex]\( y \)[/tex] represents the mass of the tree in kilograms after [tex]\( x \)[/tex] years.
The "starting mass" refers to the mass of the tree at the time when it was planted, which corresponds to [tex]\( x = 0 \)[/tex]. Therefore, we substitute [tex]\( x = 0 \)[/tex] into the equation to find the starting mass.
Let's substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[
y = 40 \cdot 1.5^x \\
y = 40 \cdot 1.5^0
\][/tex]
Recall the mathematical rule that any non-zero number raised to the power of 0 is 1. Thus:
[tex]\[
1.5^0 = 1
\][/tex]
So the equation simplifies to:
[tex]\[
y = 40 \cdot 1 \\
y = 40
\][/tex]
Therefore, the starting mass of the tree is 40 kilograms. Given the available options:
(A) 40 kg
(B) 1 kg
(C) 1.5 kg
(D) 0 kg
The correct answer is:
(A) 40 kg
