Answer:
the value of T that satisfies the equation 644 204 = 400 000(1+10%) is approximately 6.45.
Explanation:
We can simplify the equation 644 204 = 400 000(1+10%) by first simplifying the percentage term on the right-hand side:
10% of 400 000 is equal to 0.1 × 400 000 = 40 000.
So the equation becomes:
644 204 = 400 000(1 + 0.1 × 1)
Now, we can use logarithms to solve for T:
T = log(base 1.1)(644204/400000)
Using a calculator, we can evaluate the right-hand side to be approximately 0.2, so:
T = log(base 1.1)(1.61051)
Using the change of base formula, we can rewrite this as:
T = ln(1.61051) / ln(1.1)
Evaluating the natural logarithms using a calculator, we get:
T ≈ 6.45