High School

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------------------------------------------------ Solve for \( t \) in the equation:

\[ 20000 = 15000(1.072)^t \]

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)