Answer :
The solution is approximately t ≈ 3.437.
To solve the equation 20000=15000[tex](1.072)^t[/tex], we need to isolate the variable t. Here are the steps:
Divide both sides of the equation by 15000:
20000/15000 = (1.072)^t
This simplifies to:
4/3 = [tex](1.072)^t[/tex]
Take the natural logarithm (ln) of both sides to solve for t:
ln(4/3) = ln([tex](1.072)^t[/tex])
Using the properties of logarithms, we get:
ln(4/3) = t × ln(1.072)
Isolate t by dividing both sides by ln(1.072):
t = ln(4/3) / ln(1.072)
Calculating the values using a calculator, we find:
t ≈ 3.437
Therefore, the solution to the equation 20000=15000[tex](1.072)^t[/tex] is approximately t ≈ 3.437.
The complete question is:
20000=15000[tex](1.072)^t[/tex]t, find t.
20,000 = 15,000 (1.072)^t
Divide each side by 15,000 : 4/3 = (1.072)^t
Take the log of each side: log(4/3) = t log(1.072)
Divide each side by log(1.072): t = log(4/3) / log(1.072)
0.12494 / 0.03019 = 4.138 (rounded)
