 Solution

An experience curve models unit cost as $C(Q)=C_0(Q/Q_0{)}^{-b}$, where $Q$ is cumulative production. A doubling reduces cost by a fraction $1-2^{-b}$. For an illustrative twenty-percent reduction per doubling, $b=-{\log }_2(0.8)\simeq 0.322$, so four doublings would reduce the fitted cost to $0.8^4\simeq 0.41$ of its initial value.

Photovoltaic modules are manufactured in large numbers with repeated designs, so manufacturing yield, scale, automation and material use can all produce observable learning. Wind turbines also benefit from repeated manufacture, but installation, foundations, access, grid connection and site quality form a larger project-specific share; moving into poorer or more difficult sites may offset improvements. Nuclear reactors have fewer repetitions, long project times, changing designs and regulation, and substantial site and financing costs. A cumulative-capacity curve can therefore hide rather than explain changes in nuclear project cost.

A experience curve is an empirical conditional relationship, not a physical law guaranteeing success. Input prices, policy, financing, saturation of a manufacturing improvement and the definition of system boundary all affect extrapolation. Declining cost may encourage deployment, which then increases the cumulative-production variable, so correlation alone does not establish a one-way causal effect. Forecasts should test multiple learning rates and distinguish module or turbine cost from the cost of a reliable delivered electricity system.