SOLUTION: hey heres another problem i need help on. The chapter im on is called exponential and logarithmic functions. The problem is on writing an exponential function from 2 points on the

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: hey heres another problem i need help on. The chapter im on is called exponential and logarithmic functions. The problem is on writing an exponential function from 2 points on the      Log On

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Question 131700: hey heres another problem i need help on. The chapter im on is called exponential and logarithmic functions. The problem is on writing an exponential function from 2 points on the functions graph.
heres the problem
Write an exponential function of the form y=ab^x that includes the given points: (-1, 2/9) (1,2)
Thanks
Answer by jim_thompson5910(28593) About Me  (Show Source):
You can put this solution on YOUR website!
y=ab%5Ex Start with the given equation


2%2F9=ab%5E%28-1%29 Plug in x=-1, and y=2%2F9


2%2F9=a%2Fb Rewrite ab%5E%28-1%29 as a%2Fb


2b=9a Cross multiply

b=9a%2F2 Divide both sides by 2 to isolate b


y=ab%5Ex Now go back to the original equation


2=ab%5E1 Plug in x=1 and y=2

2=ab Simplify


2=a%289a%2F2%29 Plug in b=9a%2F2


4=9a%5E2 Multiply both sides by 2

4%2F9=a%5E2 Divide both sides by 9


sqrt%284%2F9%29=a Take the square root of both sides


a=2%2F3 Simplify


b=9%282%2F3%29%2F2 Plug this answer into this equation


b=%2818%2F3%29%2F2 Multiply


b=6%2F2 Reduce


b=3 Reduce again



--------------------------------
So our values are

a=2%2F3 and b=3


which means that the equation is

y=%282%2F3%29%2A3%5Ex