1. **Problem Statement:** Determine which exponential formulas correspond to the curves labeled IV, V, and VI on the graph. 2. **Given formulas:** (a) $10(1.02)^t$ (b) $20(1.02)^t$ (e) $30(0.95)^t$ (\beta) $10(1.05)^t$ (d) $30(0.85)^t$ (\phi) $30(1.05)^t$ 3. **Understanding the graph:** - Curve IV: Steep upward curve (rapid growth) - Curve V: Mostly flat, slightly decreasing (slow decay) - Curve VI: Gradual upward curve (moderate growth) 4. **Analyzing each formula:** - Formulas with base greater than 1 represent growth. - Formulas with base less than 1 represent decay. 5. **Match curves to formulas:** - IV (steep growth): Among growth formulas, $10(1.05)^t$ and $30(1.05)^t$ have the highest growth rate (1.05). Since IV is steep, it likely corresponds to $30(1.05)^t$ (\phi). - V (slightly decreasing): Decay formulas are $30(0.95)^t$ (e) and $30(0.85)^t$ (d). Since V is only slightly decreasing, $30(0.95)^t$ (e) fits best. - VI (gradual growth): Growth formulas with smaller base growth rate $10(1.02)^t$ (a) or $20(1.02)^t$ (b). VI is gradual, so $20(1.02)^t$ (\beta) fits well. 6. **Final assignment:** - IV: $30(1.05)^t$ (\phi) - V: $30(0.95)^t$ (e) - VI: $20(1.02)^t$ (\beta) 7. **Answer choice matching:** - Option (c) ɸ, ε, and δ corresponds to IV, V, and VI respectively, but δ is $30(0.85)^t$ which is a stronger decay, not gradual growth. - Option (d) β, χ, and ɸ does not fit the labels. Since the problem's options are ambiguous, the best match based on the analysis is: IV = ɸ ($30(1.05)^t$), V = ε ($30(0.95)^t$), VI = β ($20(1.02)^t$). Hence, the correct formulas representing IV, V, and VI are $30(1.05)^t$, $30(0.95)^t$, and $20(1.02)^t$ respectively.