Recognize constant percent growth or decay as evidence for an exponential model.
Reason backward in an exponential model
Problem
For the model \(f(x)=a(1.25)^x\), a value of \(125\) is known at time \(1\). Find the value \(1\) interval earlier.
Big Picture
What this problem is really about
Moving backward through an exponential model requires undoing the forward multiplier, not subtracting it. We’ll express one forward interval as multiplication by the base, reverse that operation with division, and apply it once to the known later value. Multiplying the recovered value forward again will check the reversal.
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