Question

What would the base of an exponential function with a growth rate of 7% would be 

Answer 1

The base of an exponential function with a growth rate of 7% would be 1.07, since an exponential growth function is written as y = a · b^x, and this base is determined by adding 1 to the percentage growth rate as a decimal.

Step-by-step explanation:

The base of an exponential function that represents a growth rate of 7% would be 1.07. This is because an exponential growth function is typically in the form y = a · bx, where a is the initial amount, b is the base or growth factor, and x is the time. The growth factor b is calculated by adding 1 to the decimal form of the percentage growth rate, thus 7% as a decimal is 0.07, and when we add 1 to it, we get a growth factor or base of 1.07.

For example, if you wanted to calculate the amount after 10 years, you would use the equation y = a · 1.0710. This incorporates the constant growth rate over the 10-year period. According to the rule of 70, a system growing at 7% per year would take approximately 10 years to double in size.

Answer 2

Step-by-step explanation: To check if an exponential function is increasing or decreasing you have to look at the base and at a coefficient next to the exponent.

explanation: Let y=a⋅bx

be an exponential function.

It can be:

Increasing if (a>0 and b>1) or (a<0

and b∈(0;1)) Decreasing if: (\a>0 and b∈(0;1)) or (a<0 and b>1)