Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.
Build an exponential function from an initial value and a growth factor
Problem
Write an exponential function with initial value \(500\) and growth factor \(1.08\). Assign \(a\) and \(b\) in \(f(t)=a\cdot~b^t\), verify \(f(0)\), and show that the ratio \(f(t+1)/f(t)\) equals the stated factor.
Big Picture
What this problem is really about
In an exponential model, the initial value is the coefficient and the per-interval multiplier is the base. We’ll assign those parameters directly, verify the start with the zero-exponent rule, and take the ratio of consecutive outputs to confirm that each one-step increase applies the stated factor.
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