3. Find the exponential function that satisfies the given conditions:

Initial value = 33, increasing at a rate of 7% per year.

A. [tex]f(t) = 7.1.07^t[/tex]
B. [tex]f(t) = 33 \cdot 1.07^t[/tex]
C. [tex]f(t) = 33 \cdot 7^t[/tex]
D. [tex]f(t) = 330.07^t[/tex]

4. Find the exponential function that satisfies the given conditions:

Initial value = 62, decreasing at a rate of 0.47% per week.

A. [tex]f(t) = 62 \cdot 0.9953^t[/tex]
B. [tex]f(t) = 62 - 1.47[/tex]
C. [tex]f(t) = 62 \cdot 1.0047^t[/tex]
D. [tex]f(t) = 0.47 \cdot 0.38^t[/tex]

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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