A radioactive substance has a continuous hourly decay rate of $21\%\text{.}$ What is the percent hourly decay rate? The opening sentence is telling us we must use an exponential model because the decay rate is a “constant percent”. The sentence goes on to tell us what kind of decay model and the percent rate of decay. The word “continuous” is telling us to use base $e\text{.}$ Therefore we can write the formula for decay as $$Ae^{kt}$$ where $k$ is the continuous decay constant $k=-0.21\text{.}$ This value is negative because we are told the $21 \%$ is a decrease. The value $A$ represents the initial amount of substance, but it was not stated. So we put a variable there to hold its place. The question is about the hourly percent decay. But, we were given the “continuous” hourly decay. These are two different things. A discrete model would look like $$Ab^{t}$$ where $b$ is the hourly growth factor we are trying to find. But both the discrete and continuous models have to predict the same behavior. Therefore the two formulas have to be equal — they have to produce the same values. $$A(b)^{t}=A(e^{-k})^t$$ Notice how the parentheses are used to show that both sides are actually the same thing. Both say $$A(\text{something})^{t} \text{.}$$ The “somethings” must be the same number. That is: $$b = e^{-k} \text{.}$$ With $k=-0.21$ then $b=$ (round to $4$ significant digits). Therefore, the percent hourly rate of decay is (include units).