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An exponential function passes through the points (0, 300) and (3, 153.6). Which model represents the...

6. An exponential function passes through the points (0, 300) and (3, 153.6). Which model represents the function?
a. f(x) = 300(0.512)^x
b. f(x) = 300(1.25)^x
c. f(x) = 153.6(0.80)^x
d. f(x) = 300(0.80)^x

Answer

Answer: d. f(x) = 300(0.80)^x

Explanation: An exponential function can be represented as f(x) = a(b)^x, where a is the initial value and b is the base. Given the point (0, 300), the initial value a is 300. To find b, use the point (3, 153.6):

153.6 = 300(b)^3

0.512 = b^3

b = 0.80

Thus, the function is f(x) = 300(0.80)^x.

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