Final answer:
The exponential model f(x)=7(4)^x can be rewritten with base e as f(x) = 7e^(x · ln(4)) by using the identity b^n = e^(n · lnb), where e is the base of natural logarithms.
Step-by-step explanation:
To express the exponential model f(x)=7(4)^x with the base e, we can leverage the fact that any base raised to a power can be written as e raised to the power of the natural logarithm of the base times the exponent. In this case, the base is 4, so we're looking for e to the power of ln(4) times x.
Therefore, the model can be rewritten as:
f(x) = 7e(x · ln(4))
This is done by using the identity that bn = e(n · lnb). Since e is the base of natural logarithms, this transformation allows us to express any exponential function with a different base in terms of e, which is approximately 2.71828.