[tex]\large\boxed{Answer:\ f(x)=11000(0.7)^x}[/tex]
[tex]f(x)=a\cdot b^x\\\\\text{Te graph passes throught the points (0, 11000) and (2, 5390).}\\\\(0,\ 11000)\to x=0,\ f(0)=11000\\\\\text{substitute:}\\\\11000=a\cdot b^0\\\\11000=a\cdot1\\\\\boxed{a=11000}\\\\\text{Therefore we have:}\\\\f(x)=11000(b^x)[/tex]
[tex](2,\ 5390)\to x=2,\ f(2)+5390.\ \text{Substitute:}\\\\5390=11000(b^2)\qquad\text{divide both sides by 11000}\\\\\dfrac{5390}{11000}=b^2\to b=\sqrt{\dfrac{539}{1100}}\\\\b=\sqrt{0.049}\\\\b=0.7[/tex]
The value of a is 11000 and the value of b is 5390 and this can be determined by using the given data.
Given :
An exponential function [tex]\rm f(x) = ab^x[/tex] passes through the points (0, 11000) and (2, 5390).
The following steps can be used in order to determine the values of 'a' and 'b':
Step 1 - Write the given function.
[tex]\rm f(x) = ab^x[/tex]
Step 2 - Now, substitute the value of x and f(x) that is (0,11000) in the above function.
11000 = a[tex]\rm b^0[/tex]
11000 = a
Step 3 - Now, again substitute the value of x and f(x) that is (2,5390) in the given function.
[tex]\rm 5390=11000\times b^2[/tex]
0.49 = [tex]\rm b^2[/tex]
b = 0.7
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https://brainly.com/question/1957976
