Final answer:
To find the correct exponential function from two points without a calculator, one must substitute the points into the general form and solve for parameters 'a' and 'b'. Squaring an exponential entails squaring the coefficient and multiplying the exponent by two.
Step-by-step explanation:
The task at hand involves finding an exponential function based on two points given to us. However, the question doesn't provide the specific points, so we are unable to calculate directly which function A), B), C), or D) is the correct exponential function using those two points. Despite this, understanding how to handle such problems is key. When dealing with an exponential function, the general form looks like f(x) = a(bx), where 'a' is the initial value and 'b' is the base of the exponential function.
To find the correct function using two points without a calculator, one would substitute the x and y values from the points into the general form of the exponential function and solve the resulting system of equations to find the values of 'a' and 'b'. For example, given two points (x1, y1) and (x2, y2), we would set up the following equations: y1 = a(bx1) and y2 = a(bx2). After solving for 'a' and 'b', one can determine the specific form of the exponential function.
When squaring an exponential, as mentioned in the context, you square the coefficient and multiply the exponent by 2, which would yield an equation like (a2)(b2x) for an initial term a(bx).
If we lack a y* calculator button, we can utilize natural logarithms (ln) for computation. For instance, to solve for x in the equation ex = 2, we could take the natural log of both sides to get ln(ex) = ln(2), which simplifies to x = ln(2) since the natural log and the exponentiation by 'e' are inverse functions.