Answer :
Final answer:
The correct exponential function for the first question is f(t) = 33 * 1.07^t, reflecting an initial value of 33 with an increasing rate of 7% per year. For the second question, the correct function is f(t) = 62 * 0.9953^t, reflecting an initial value of 62 with a decreasing rate of 0.47% per week.
Explanation:
The questions are asking for the exponential function that satisfies certain conditions, specifically an initial value and a rate of change. To find the correct function, we'll need to use the general form of an exponential function, which is f(t) = a * b^t, where a is the initial value, and b is the base that represents the rate of change.
For the first question, the initial value is 33, and it's increasing at a rate of 7% per year. So, to find the correct expression, we substitute the values in, which gives us f(t) = 33 * 1.07^t.
For the second question, the initial value is 62 and it's decreasing at a rate of 0.47% per week. This means the base should be 1 - 0.0047, making it less than 1. To find the correct expression, we substitute the values in, again, which gives us f(t) = 62 * 0.9953^t.
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