The hourly growth rate parameter is equal to 2.22%.
<h3>How to determine the hourly growth rate parameter?</h3>
In Mathematics, an exponential function simply refers to a mathematical function whose values are generated by a constant that is raised to the power of the argument.
Mathematically, an exponential function can be modeled by using this equation:
A(t) = ae^{kt}
Where:
- a represents the initial value.
- t represents time.
- k represents the rate of change or growth rate.
Based on the information provided, we have the following:
A(t) = 1100e^{6k} .....equation 1.
A(6) = 1257 .....equation 2.
Equating the two equations, we have:
1100e^{6k} = 1257
e^{6k} = 1257/1100
e^{6k} = 1.1427
Taking the natural log (ln) of both sides of the equation, we have:
6k = ln(1.1427)
6k = 0.1334
Hourly growth rate, k = 0.1334/6
Hourly growth rate, k = 0.0222
As a percentage, we have:
Hourly growth rate, k = 0.0222 × 100
Hourly growth rate, k = 2.22%.
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