Bacterius said:Yes, it is correct, if $t$ represents hours (it is not made clear in the problem what the unit of $t$ is). For instance, if $t$ was in minutes, then you need to substitute $t = 4 \times 60 = 240$. I think it is meant to be hours though.
Be careful what each symbol means. For instance, in the first question, it says "500kg of raw sugar has been refined to 380kg". Does that mean that there is 380kg of raw sugar remaining, and that there is 500 - 380 = 120kg of refined sugar, or the opposite? Or something else? (sorry, I am not familiar with sugar refining) This will affect the meaning of (and answers to) the questions.
In word problems the hardest part is often (at least to me) understanding what the problem is and converting it to math. They often have little traps built-in to confuse people and make them pay attention to wording, it can be frustrating actually.
Exponential decay is a mathematical concept that describes the decrease of a quantity over time at a constant percentage rate.
The formula for exponential decay is A(t) = A₀ * e^(-kt), where A(t) is the quantity at time t, A₀ is the initial quantity, and k is the decay constant.
To solve an exponential decay problem, you need to know the initial quantity, the decay constant, and the time at which you want to find the quantity. Then, plug these values into the formula A(t) = A₀ * e^(-kt) and solve for A(t).
The half-life is the amount of time it takes for the quantity to decrease by half. In an exponential decay problem, the half-life is represented by the value ln(2)/k, where k is the decay constant.
Some real-world examples of exponential decay include radioactive decay, population growth, and the depreciation of assets. In each of these cases, the quantity decreases at a constant percentage rate over time.