S6. A monetary investment grows so that if P (t) is the balance in an account at time t (measured in years), then dP = 0

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S6. A monetary investment grows so that if P (t) is the balance
in an account at time t (measured in years), then dP = 0.05P (t).
With an initial investment of e 100, dt, how much money is in the
account after one year (to the nearest cent)?
S7. A disc of mass m and radius R rolls down a slope of incline
60◦. The slope is rough enough to prevent slipping. The disc
travels from rest a distance 120 m down the slope. The
gravitational constant is g = 10 ms−2. Show that the final linear
velocity of the disc is 37.2 m s−1.