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cupoosta [38]
3 years ago
7

Caroline puts $400 into a savings account that earns 6% annually. Write a function that represents this situation, where t is th

e time in years. Solve algebraically after how many years she will get $1200 in her account (round it to the nearest year).
Mathematics
1 answer:
DaniilM [7]3 years ago
5 0

Answer: 19 years

Step-by-step explanation:

Given

Amount invested \$400

Rate of interest R=6\%

after 1-year amount becomes

A=400\left (1+6\%\right)\\A=400\left (1+0.06\right)\\A=400\times 1.06\\A=\$424

After n years it is

A=400\left (1.06\right)^n

Sum accumulated is \$1200

\Rightarrow 1200=400\left(1.06\right)^n\\\Rightarrow 3=\left(1.06\right)^n\\\text{Taking log both sides}\\\Rightarrow n=\dfrac{\ln 3}{\ln 1.06}\\\\\Rightarrow n=18.85\approx 19\ \text{years}

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