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The graph of the exponential function f(x) is shown below. Find f(x) in the form of $$f(x)= \frac??\cdot?^x$$ Apr 8, 2023

#1
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What are you rying to find?

Also could you please help me with the question above yours? I'm on a time limit so pls do it a fast as u can

Apr 8, 2023
#2
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The graph of an exponential function is always increasing, so we know that f(x) is increasing. We also know that f(1)=3 and f(4)=192. This means that f(x) must be a function that takes on values that are more than 3 times as large for every increase of 3 in x.

Therefore, the function that satisfies these conditions is f(x)=3^x. This function is an exponential function with a base of 3. It takes on values that are more than 3 times as large for every increase of 3 in x.

To enter the function, you can write $$f(x) = \dfrac{1}{1} \cdot 3^x$$

Apr 8, 2023
#3
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The relationship between x and y can be written in the form $$\displaystyle y=ab^{x}.$$

Taking logs, doesn't matter what base, and then making use of the laws of logs,

$$\displaystyle \log y=\log ab^{x}=\log a + \log b^{x} =\log a + x\log b.$$

Substitute the two sets of co-ordinates,

$$\displaystyle \log 3 = \log a +1.\log b, \dots \dots(1) \\ \log 192=\log a + 4\log b.\dots..(2)$$

Now solve simultaneously for a and b.

Start by subtracting (1) from (2), (and notice that 192 = 3.64 = 3.4^3).

Apr 9, 2023