$\"\"$

\

(a)

\

Write a continuous exponential equation to price.

\

If an initial quantity $\"\"$ grove or decays at an exponential rate $\"\"$ or $\"\"$ , then the final amount $\"\"$ after a time $\"\"$ is given by the following formula $\"\"$ .

\

Coffee chain’s stock during first year of trading is $\"\"$ .

\

Coffee chain’s stock during first year of trading is $\"\"$ .

\

Time period $\"\"$ is $\"\"$ .

\

Here time period is $\"\"$ .

\

Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

Apply logarithm on each side.

\

$\"\"$

\

Power property of logarithm : $\"\"$ .

\

$\"\"$

\

Apply property of logarithm : $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Continuous exponential equation to price is $\"\"$ .

\

$\"\"$

\

(b)

\

Find number of stores after $\"\"$ year.

\

Find time period $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

Price of the stock during the $\"\"$ year of trading is $\"\"$ .

\

$\"\"$

\

(a) Continuous exponential equation to price is $\"\"$ .

\

(b) Price of the stock during the $\"\"$ year of trading is $\"\"$ .