$\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill &75000\\ P=\textit{initial amount}\dotfill &400000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &39\\ \end{cases} \\\\\\ 75000=400000(1 - \frac{r}{100})^{39}\implies \cfrac{75000}{400000}=\left( \cfrac{100-r}{100} \right)^{39}$

$\cfrac{3}{16}=\left( \cfrac{100-r}{100} \right)^{39}\implies \sqrt[39]{\cfrac{3}{16}}=\cfrac{100-r}{100}\implies 100\sqrt[39]{\cfrac{3}{16}}=100-r \\\\\\ r=100-100\sqrt[39]{\cfrac{3}{16}}\implies r\approx 4.2$

4 0

2 years ago

Read 2 more answers

eight times the result of subtracting 3 from a number is equal to the number increased by 25 what is the number

polet [3.4K]

Answer=7

Lets write the an equation for the information given
8(x-3)=x+25
subtract x from both sides
8(x-3)-x=25
8x-24-x=25
7x-24=25
add 24 to both sides
7x=49
divide both sides by 7
x=7

5 0

2 years ago

Read 2 more answers