In India, the newspapers are reporting that without lockdown $1$ person will infect $406$ persons in $30$ days. The newspapers are also reporting that the Mathematical factor for this growth is $1.5$ to $4$. I tried to figure this out by plugging in the details in the compounding formula, and I found that the factor should be $6.65$. What am I doing wrong?
I tried to solve the problem in the following way:
$$\left(1 + \frac{6.65}{30}\right)^{30} \approx 406.$$
On
Remember the general form of the exponential equation
$$ab^x = y$$
Since our starting value is $1$, we set $a = 1.$ Now, if we let $x$ represent time (in days), we can set $x=30$, since $406$ people are infected every 30 days. Thus, we solve the equation
$$b^{30}=406$$ $$b = 406^{1/30}$$ $$\approx 1.22166$$
Thus we have
$$1.22166^x = y$$
You are dividing 6.65 people by 30, which doesn't make sense. You do that for interest rates, an interest rate of 6.65 per month compounded daily, we divide 6.65 by 30, then pay that amount each day. Not applicable for disease transmission. The $R_0$ factor is not "people per month", so we do not get "people per day" by dividing $R_0/30$.