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Use the image to answer the question Lincoln's parents invested $5,000 in a college savings account when he was born. If the account has a growth rate of 12%, the situation can be modeled by the equation a(t)= 5,000(1.12)t , where a is the amount after t years. Which one of the following statements is true about the graph of the function? Option #1: As t increases, a increases slowly at first and then quickly. Option #2: As t increases, a increases quickly at first and then slowly.
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The equation given, \( a(t) = 5,000(1.12)^t \), represents exponential growth. In this case, the amount \( a \) increases as \( t \) (the number of years) increases.
For exponential functions, the growth appears to be slow at first, but as time passes, the growth rate accelerates, resulting in a more rapid increase in the later years.
Therefore, the true statement regarding the graph of the function is:
Option #1: As t increases, a increases slowly at first and then quickly.
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