We study the costs and benefits of plasticity by evolving agents in environments with different rates of environmental change. Evolution allows both hard-coded strategies and learned strategies, with learning rates varying throughout life. We observe a range of change rates where the balance of costs and benefits are just right for evolving learning. Inside this range, we see two separate strategies evolve: lifelong plasticity and sensitive periods of plasticity. Sensitive periods of plasticity are found to reduce the learning cost while retaining the benefits of learning. This affects the evolutionary process, by limiting genetic assimilation of learned characteristics, making agents able to remain adaptive after relatively long periods of environmental stability.