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------------------------------------------------ If [tex]f(4) = 246.4[/tex] when [tex]r = 0.04[/tex] for the function [tex]f(t) = Pe^{rt}[/tex], then what is the approximate value of [tex]P[/tex]?

A. 210
B. 1220
C. 50
D. 289

To find the approximate value of P, given f(4) = 246.4 for the function f(t) = Pe^rt at r = 0.04, the values are substituted and solved to reveal that P is approximately 209.88, which is closest to the provided option (a) 210.

Therefore, the correct option is a.

Explanation:

The student has asked: If f(4) = 246.4 when r = 0.04 for the function f(t) = Pert, then what is the approximate value of P? In order to find the value of P, we need to substitute the given values into the function and solve for P. The function is given as:
f(t) = Pe^rt

Substituting the given values, we have:

246.4 = P * e(0.04*4)

Now, we solve for P:

246.4 = P * e0.16

To isolate P, divide both sides of the equation by e0.16:

P = 246.4 / e0.16

Using a calculator, we find that e0.16 is approximately 1.174, so:

P = 246.4 / 1.174

P ≈ 209.88

The closest answer to this approximation is option (a) 210.