Answer:
8 years
Step-by-step explanation:
Tim's account balance has an initial value of $6400 and is multiplied yearly by the factor 1.01. Thus, it can be described by the exponential equation ...
b = 6400·1.01^t
where b is the balance after t years.
Putting in the desired balance, we can find t.
6900 = 6400·1.01^t
1.078125 = 1.01^t . . . . . divide by 6400
log(1.078125) = t·log(1.01) . . . . take the logarithm of both sides
log(1.078125)/log(1.01) = t ≈ 7.56 ≈ 8 . . . . . divide by the coefficient of t
It will take Tim approximately 8 years to reach a balance of $6900.
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The problem can also be solved using a graphing calculator.
