Kylie invested $290 in an account paying an interest rate of 2.5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $390?

t= 11.9

Step-by-step explanation:

Compounded Continuously:

A=Pe^{rt}

A=Pe  

rt

A=390\hspace{35px}P=290\hspace{35px}r=0.025

A=390P=290r=0.025

Given values

390=

390=

\,\,290e^{0.025t}

290e  

0.025t

Plug in

\frac{390}{290}=

290

390

​  

=

\,\,\frac{290e^{0.025t}}{290}

290

290e  

0.025t

​  

Divide by 290

1.3448276=

1.3448276=

\,\,e^{0.025t}

e  

0.025t

\ln\left(1.3448276\right)=

ln(1.3448276)=

\,\,\ln\left(e^{0.025t}\right)

ln(e  

0.025t

)

Take the natural log of both sides

\ln\left(1.3448276\right)=

ln(1.3448276)=

\,\,0.025t

0.025t

ln cancels the e

\frac{\ln\left(1.3448276\right)}{0.025}=

0.025

ln(1.3448276)

​  

=

\,\,\frac{0.025t}{0.025}

0.025

0.025t

​  

Divide by 0.025

11.8506326=

11.8506326=

\,\,t

t

t\approx

t≈

\,\,11.9

11.9

Round to the nearest tenth of a year

i dont have an answer

step-by-step explanation:

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet