Question

Find the exponential function that satisfies the given conditions:
Initial value = 34, increasing at a rate of 7% per year

Answer 1

generic exponential function format:

ab^(x)

if we consider the independent variable to be time, as we are here, we can change x to t to get

ab^(t)

where a is the initial value, and b is the growth factor. the initial value is already given as 34. now, since it's increasing at a rate of 7% per year, we can represent this growth as 100% + 7% (remember, we can't just multiply by 7% because it retains 100% of its value, plus an additional 7%)

therefore, b = 100% + 7%, or as a decimal, 1 + 0.07 = 1.07

plug in your a and b values into the equation and see which equation matches. **important** do not multiply a and b together.