Answer:
[tex]\textsf{1.\;\;Equation:\quad$A=720(1.048)^{t}$}[/tex]
[tex]\textsf{Solution:\quad$\$1263.77$}[/tex]
[tex]\textsf{2.\;\;Equation:\quad$y=2^x$}[/tex]
[tex]\textsf{Solution:\quad$8$}[/tex]
Step-by-step explanation:
Question 1
Assuming the account earns annual compound interest.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ A=P\left(1+r\right)^{t}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given values:
Substitute the given values or P and r into the annual compound interest formula to create an equation for the amount of money in the account after t years:
[tex]\implies A=720(1+0.048)^{t}[/tex]
[tex]\implies A=720(1.048)^{t}[/tex]
To find the amount of money in the account after 12 years, substitute t = 12 into the equation:
[tex]\implies A=720(1.75523549...)[/tex]
[tex]\implies A=1263.76955...[/tex]
[tex]\implies A=1263.77[/tex]
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Question 2
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Given values:
- a = 1 (initial number of bacteria)
- b = 2 (as the bacteria doubles)
Substitute the given values or a and b into the exponential function formula to create an equation for the number of bacteria after x days:
[tex]\implies y=1(2)^x[/tex]
[tex]\implies y=2^x[/tex]
To find the number of bacteria after 3 days, substitute x = 3 into the equation:
[tex]\implies y=2^3[/tex]
[tex]\implies y=8[/tex]
