High School

If \( f(x) \) is an exponential function of the form \( y = ab^x \), where \( f(-4.5) = 21 \) and \( f(0.5) = 82 \), then find the value of \( f(-2) \) to the nearest hundredth.

Answer :

Answer:

41.50

Step-by-step explanation:

(82=ab^.5)/*(21=ab^-4.5)=3.90476190476

3.90476190476^(1/5)=1.31316382875

82=a(1.31316382875)^.5

82=a(1.14593360573)

82/1.14593360573=a

a=71.557374345

Equation: y= 71.557374345(1.31316382875)^x

f(-2): y= 71.557374345(1.31316382875)^-2=41.4969878424, 41.50 rounded

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