Assuming that n 1 , rewrite the compound interest equation B t 900 1.185 t in the general form.

Mathematics

1 answer:

Rufina [12.5K]3 years ago

3 0

$\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\\
r=rate\to r\%\to \frac{r}{100}\\
n=
\begin{array}{llll}
\textit{times it compounds per year}
\end{array}\\
t=year
\end{cases}$

$\bf 1.185\implies 1+0.185\qquad\quad and\quad n=1
\\\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}\implies A=P\left(1+0.185\right)^{nt}\implies A=P\left(1+\frac{0.185}{1}\right)^{1\cdot t}$

so, the percentage of the rate is 0.185, what's that as a percentage? well, 0.185 * 100, 18.5%.

You might be interested in

I really need help with this one please

natka813 [3]

The distance from the sun is option 2 5.59 astronomical units.

Step-by-step explanation:

Step 1; To solve the question we need two variables. P which represents the number of years a planet takes to complete a revolution around the Sun. This is given as 13.2 years in the question so P = 13.2 years. The other variable is the distance between the planet and the sun in astronomical units. We need to determine the value of this using the given equation.

Step 2; So we have to calculate the value of 'a' in Kepler's equation. But the exponential power $\frac{3}{2}$ is on the variable we need to find so we multiply both the sides by an exponential power of $\frac{2}{3}$ to be able to calculate 'a'.

P = $a^{\frac{3}{2} }$ , $P^{\frac{2}{3} }$ = $a^{\frac{3}{2}*\frac{2}{3} }$ , $P^{\frac{2}{3} }$ = a, $13.2^{\frac{2}{3} }$ = a = 5.58533 astronomical units.