Question

LOTS OF POINTS IM DESPERATE! can someone please refresh my memory on a couple of log equations? Thank you!

Answer 1

Answer:

78.  t=8.66yrs

79.  r=23.10%

80. r=11.0975%

Step-by-step explanation:

78. Given the initial deposit is $1,000 and the 8% compounded continuously. The doubling time can be calculated using the formula;

$A=Pe^{it}$

Given that A=2P, we substitute in the equation to solve for t:

$A=Pe^{rt}\\\\2P=Pe^{rt}\\\\2=e^{0.08t}\\\\0.08t=\ In 2\\\\t=8.66\ years$

Hence, it takes 8.66 years  for $1,000 to double in value.

79.

Given the initial deposit is $1,000 and the r% compounded continuously.

-The doubling rate can be calculated using the formula;

$A=Pe^{rt}$

#We substitute our values in the equation to solve for r:

$A=Pe^{rt}\\\\A=2P, t=3\\\\\therefore\\\\2P=Pe^{3r}\\\\2=e^{3r}\\\\r=\frac{In \ 2}{3}\\\\=0.23105\approx 23.10\%$

Hence, the deposit will double in 3 years at a rate of 23.10%

80.

Given the initial deposit is $30,000 and the future value is $2,540,689.

-Also, given t=40yrs, the rate of growth for continuous compounding is calculated as:

$A=Pe^{rt}, \ \ \ r=r, t=40yrs\\\\2540689=30000e^{40r}\\\\\frac{2540689}{30000}=e^{40r}\\\\r=\frac{In \ (2540689/30000)}{40}\\\\\\=0.110975=11.0975\%$

Hence, the deposit will grow at a rate of approximately 11.0975%