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So, current = initial × (0.997)^10
Let initial = x
Then 2000 = x × (0.997)^10
So x = 2000 / 0.9703 ≈ 2061.8
Therefore, the ratio 10,000 years ago was approximately 2061.8 ppm.
#### 2061.8
A science educator designs a physics simulation where a virtual cart accelerates at a rate doubling every 2 seconds, starting at 0.5 m/s². What is the cart’s acceleration after 10 seconds?
Acceleration doubles every 2 seconds: this is exponential growth: a(t) = a₀ × 2^(t/2)
a₀ = 0.5 m/s², t = 10 s
a(10) = 0.5 × 2^(10/2) = 0.5 × 2^5 = 0.5 × 32 = 16 m/s²