Exponential growth and decay

Which of the following functions satisfies the differential equation $\dfrac{dy}{dt} = 3y$?

A quantity $y(t)$ satisfies $y'(t) = 3y(t)$ for all $t$, and $y(0) = 4$. Find $y(1)$.

A bacterial culture has population $P(t) = 5e^{0.2t}$ million after $t$ hours. How long does it take the population to double?

A radioactive isotope decays so that 30 % of any sample is gone after 10 days. How long does it take for a 200 g sample to decay to 50 g?

A yeast culture grows at a rate proportional to its size, and increases by 50 % every 4 hours. What is its doubling time?

A mug of tea at 90 °C is left in a room held at 20 °C. After 5 minutes it has cooled to 60 °C. Assuming Newton's law of cooling, when will the tea reach 30 °C?

An object's temperature is $T(t) = 24 + 60e^{-0.1t}$ degrees Celsius after $t$ minutes. Which differential equation does $T$ satisfy, and what is the room temperature?

A kettle of water at 100 °C is left to cool in a room of unknown constant temperature. After 10 minutes the water is at 80 °C, and after 20 minutes it is at 65 °C. Assuming Newton's law of cooling, find the room temperature.

A savings account pays 4 % per year, compounded continuously, and its owner deposits money continuously at \$3000 per year. The balance $A(t)$ therefore satisfies $A'(t) = 0.04A + 3000$. If the account opens with \$20 000, what is the balance after 10 years?

A retiree has \$100 000 in an account paying 5 % per year, compounded continuously, and withdraws money continuously at \$6000 per year, so the balance satisfies $A'(t) = 0.05A - 6000$. Solve for $A(t)$, and find how many years it takes for the money to run out.