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Galina-37 [17]
2 years ago
12

Terri invested $1500 in an account with an interest rate of 2.25% compounded continuously. How long will it take for Teri’s acco

unt to earn $5000
Mathematics
1 answer:
melomori [17]2 years ago
7 0

Answer:

53.51 years

Step-by-step explanation:

FV = PV e⁽ⁿˣ⁾

FV = Future Value = $5000

PV = Present Value = $1500

n = Interest Rate = 2.25%

x = time in years = ?

e = mathematical constant = 2.7183

So,

5000 = 1500 e⁽⁰°⁰⁰²⁵ˣ⁾

50 / 15 = e⁽⁰°⁰⁰²⁵ˣ⁾

㏑ (3.3333) = 0.0225x ㏑ (2.7183)

1.2040 = 0.0225x

x = 53.51 year

So, If compounded continuously at an APR of 2.25% the amount invested in an account of $1500 will accumulate to $5000 in 53.51 years.

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A model for the population in a small community after t years is given by P(t)=P0e^kt.
LUCKY_DIMON [66]
\bf \textit{Amount of Population Growth}\\\\
A=Ie^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\\
\end{cases}

a)

so, if the population doubled in 5 years, that means t = 5.  So say, if we use an amount for "i" or P in your case, to be 1, then after 5 years it'd be 2, and thus i = 1 and A = 2, let's find "r" or "k" in your equation.

\bf \textit{Amount of Population Growth}\\\\
A=Ie^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &2\\
I=\textit{initial amount}\to &1\\
r=rate\\
t=\textit{elapsed time}\to &5\\
\end{cases}
\\\\\\
2=1\cdot e^{5r}\implies 2=e^{5r}\implies ln(2)=ln(e^{5r})\implies ln(2)=5r
\\\\\\
\boxed{\cfrac{ln(2)}{5}=r}\qquad therefore\qquad \boxed{A=e^{\frac{ln(2)}{5}\cdot t}} \\\\\\
\textit{how long to tripling?}\quad 
\begin{cases}
A=3\\
I=1
\end{cases}\implies 3=1\cdot e^{\frac{ln(2)}{5}\cdot t}

\bf 3=e^{\frac{ln(2)}{5}\cdot t}\implies ln(3)=ln\left( e^{\frac{ln(2)}{5}\cdot t} \right)\implies ln(3)=\cfrac{ln(2)}{5} t
\\\\\\
\cfrac{5ln(3)}{ln(2)}=t\implies 7.9\approx t

b)

A = 10,000, t = 3

\bf \begin{cases}
A=10000\\
t=3
\end{cases}\implies 10000=Ie^{\frac{ln(2)}{5}\cdot 3}\implies \cfrac{10000}{e^{\frac{3ln(2)}{5}}}=I
\\\\\\
6597.53955 \approx I
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3 years ago
Write 3.6 in a word form
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Three and six tenths

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3 years ago
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Answer:

66

Step-by-step explanation:

71+43=114

180-114=66

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How many 5 minutes intervals are there in 1 ¼ hours?​
katrin [286]

Answer:

1 1/4 hours=60+15 minutes =75 minutes

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Maths help please!!!!!! PART B ONLY
andreyandreev [35.5K]

Answer:

19.37.

Step-by-step explanation:

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x^4/4 - 5x^3/3 + x^2 + 8x

Area under the curve from x = -1 to x = 0

= (-1)^4/4 - 5(-1)^3/3 + (-1)^2 - 8

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Total = 15.75.

Now we subtract 12.13 to get the area  from x = 2 to x =p.

= 15.75 - 12.13 = 3.62

So total shaded area = 15.75 + 3.62

= 19.37.

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2 years ago
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