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Andreyy89
3 years ago
7

Suppose f is a function with exponential growth and f(0)=1. Explain why f can be represented by a formula of the form

Mathematics
2 answers:
galben [10]3 years ago
7 0

We are supposed to explain why the given function can be expressed in form f(x)=b^{x}, when f(0)=1.

Since the given function is an exponential function we can express it as  f(x)=a(b)^{x}.

Now let us substitute x=0 in the given function,  

f(x)=b^{x}

f(0)=b^{0}  

f(0)=1  

Let us substitute x=0 in our function.    

f(0) = a(b)^{0}    

f(0) = a\cdot 1                    

f(0)=a  

Upon substituting a=1 in our function we will get,

f(x) = 1(b)^{x}

f(x) =(b)^{x}

Therefore, our function f can be represented by the formula of the form f(x)=b^{x}.

Firdavs [7]3 years ago
6 0

Answer: Because, here the rate of change is directly  proportional to the value of f(x) and it is satisfying the condition f(0)=1.

Explanation:

Since, Given function= f(x)= b^x, where b>1

let b=1+n where n is any positive number.

Thus, f(x)=(1+n)^x is an exponential function.( because its value is raising by the power of a constant 1+n )

And, for x=0, f(0)=(1+n)^0⇒f(0)=1

let n=1,  f(x) =2^x after making its graph we found that the function is growing and growth rate is positive.

Similarly, function f will be growing exponential for the every value of n. where f(0)=1.



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