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Liam opened a savings account and deposited $6000. The account earns 5% in interest annually. He makes no further deposits and does not withdraw any money. In t years, he has $8865 in this account. Write an equation in terms of t that models the situation.

Liam opened a savings account and deposited $6000 \$ 6000 . The account earns 5% 5 \% in interest annually. He makes no further deposits and does not withdraw any money. In t t years, he has $8865 \$ 8865 in this account.\newlineWrite an equation in terms of t t that models the situation.

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Q. Liam opened a savings account and deposited $6000 \$ 6000 . The account earns 5% 5 \% in interest annually. He makes no further deposits and does not withdraw any money. In t t years, he has $8865 \$ 8865 in this account.\newlineWrite an equation in terms of t t that models the situation.
  1. Convert to Decimal: Write 5%5\% as a decimal.5%5\% can be converted to a decimal by dividing by 100100.5%=5100=0.055\% = \frac{5}{100} = 0.05
  2. Exponential Growth Formula: Identify the formula for exponential growth.\newlineThe formula for exponential growth in this context is A=P(1+r)tA = P(1 + r)^t, where:\newlineAA is the amount of money accumulated after nn years, including interest.\newlinePP is the principal amount (the initial amount of money).\newlinerr is the annual interest rate (decimal).\newlinett is the time the money is invested for, in years.
  3. Substitute Given Values: Substitute the given values into the formula.\newlineWe know that P=$6000P = \$6000, r=0.05r = 0.05, and A=$8865A = \$8865.\newlineWe want to find the equation in terms of tt, so we will leave tt as the variable.\newlineA=P(1+r)tA = P(1 + r)^t becomes 8865=6000(1+0.05)t8865 = 6000(1 + 0.05)^t.
  4. Simplify Equation: Simplify the equation.\newline1+0.05=1.051 + 0.05 = 1.05, so the equation becomes 8865=6000(1.05)t8865 = 6000(1.05)^t.\newlineThis is the equation that models the situation.

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