Please help?

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1 Answer
Dec 18, 2017

#x = 5 => a = 12 #

Explanation:

To solve this problem we must recal what an exponential function actually is:

#y = ab^x # is an exponential function, where #a,b in RR#
(meaning a and b are constants )

We know #(3,8) and (7,18) # satisfy the function:

#8 = ab^3 # and # 18 = ab^7 #

Now we can solve symoltaneously:

#=> a = 8/(b^3) and a = 18/(b^7) #

#=> 8/(b^3) = 18/(b^7) #

#=> b^4 = 9/4 #

#=> b^2 = 3/2 #

#=> b = sqrt(3/2) #

To find #a#:

#=> 8 =a * (sqrt(3/2))^3 #

#=> 8/(sqrt(3/2)^3 ) = a #

Hence our function is #y = 8/((sqrt(3/2))^3 ) *( sqrt(3/2)) ^x #

Hence using a calculator and plugging in #x=5# we get #a = 12 #