1. **State the problem:** Amoebae double every hour. Starting with 1 amoeba, find how many amoebae there will be after 7 hours. 2. **Formula used:** The number of amoebae after $t$ hours when doubling every hour is given by the exponential growth formula: $$N = N_0 \times 2^t$$ where $N_0$ is the initial number of amoebae and $t$ is the time in hours. 3. **Apply the formula:** Here, $N_0 = 1$ and $t = 7$. $$N = 1 \times 2^7$$ 4. **Calculate:** $$2^7 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 128$$ 5. **Final answer:** There will be **128 amoebae** at the end of 7 hours.