Question

Inversion is one step in processing raw sugar. Suppose that in this process, 20% of the available raw sugar is changed to a refined sugar every 5 hrs. If a process begins with 3,000 pounds of raw sugar, write an exponential equation for the amount A of raw sugar (in pounds) t hrs after the process begins. How many hours must elapse before there are 50 pounds of raw sugar?

Answer 1

To write the exponential equation for the amount A of raw sugar (in pounds) t hours after the process begins, we use the equation A = 3000 * (0.8)^(t/5). To find out how many hours must pass before there are 50 pounds of raw sugar, we set up the equation 50 = 3000 * (0.8)^(t/5) and solve for t.

Step-by-step explanation:

To write the exponential equation for the amount A of raw sugar (in pounds) t hours after the process begins, we need to consider that 20% of the available raw sugar is changed to refined sugar every 5 hours.

The amount of raw sugar after t hours can be represented by the equation: A = 3000 * (0.8)^(t/5).

To find out how many hours must elapse before there are 50 pounds of raw sugar, we can set up the equation: 50 = 3000 * (0.8)^(t/5) and solve for t.

By taking the logarithm of both sides, we get t/5 = log(50/3000) / log(0.8). Solving for t, we find that t is approximately 8.72 hours.