The number of visitors to your business website increased at a rate of 60% per day, going from 30 per day to 30,000 per day. How many days did it take to go from 30 to 30,000 visitors per day?
30,000(1+0.6)
but I need to solve for t that's where I get lost.
30(1.6)^n = 30000
1.6^n = 1000
n log 1.6 = log 1000
n = log1000/log1.6 = 14.7
15
To solve for the number of days it took for the number of visitors to increase from 30 to 30,000, we can set up an equation.
Let's say t represents the number of days it took. On the first day, the number of visitors is 30, and after t days, the number of visitors is 30,000.
We can use the formula for compound interest or exponential growth: A = P(1 + r)^t, where A is the final amount, P is the initial amount, r is the growth rate, and t is the number of time periods.
In this case, we have:
A = 30,000 (final amount)
P = 30 (initial amount)
r = 0.6 (growth rate)
t = unknown (the number of days we are trying to find)
Substituting these values into the formula, we get:
30,000 = 30(1 + 0.6)^t
To solve for t, we need to isolate it on one side of the equation. Here are the steps to solve it:
1. Divide both sides by 30:
30,000 / 30 = (1 + 0.6)^t
2. Simplify:
1,000 = (1.6)^t
3. Take the logarithm of both sides. You can use logarithm base 10 (log) or natural logarithm base e (ln), depending on your preference or calculator:
log(1,000) = log((1.6)^t) or ln(1,000) = ln((1.6)^t)
4. Apply the logarithmic property to bring the exponent down:
log(1,000) = t * log(1.6) or ln(1,000) = t * ln(1.6)
5. Divide both sides by log(1.6) or ln(1.6):
t = log(1,000) / log(1.6) or t = ln(1,000) / ln(1.6)
Now, calculate either of those expressions to find the value of t.