Question

O EXPONENTIAL AND LOGARITHMIC FUNCTIONS Finding the time to reach a limit in a word problem on... Savanah A laptop computer is purchased for $3000. Each year, its value is 70% of its value the year before. After how many years will the laptop computer be worth $600 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer. 1 years X 5 ?

Answer 1

Answer:

Data given:

Purchasing cost of the laptop computer, P = $3000

Each year, its value is 70% of its value the year before.

Number of years it will take for the laptop to be worth $600 or less = ?

Based on the given information, we can say that the given problem can be modeled using a decaying exponential function as -

where P - purchasing cost of the laptop computer i.e. cost at time t = 0

Using the above function, we can find the number of years it will take for the laptop to be worth $600 or less as -

$C(t) \leq 600$

$3000(0.7)^{t} \leq 600$

$(0.7)^{t} \leq 0.2$

$t \geq \log_{0.7}0.2$

$t \geq \frac{\log_{10}0.2}{\log_{10}0.7}$$(From \ logarithm \ property: \ \ \ \log_{a}b = \frac{\log b}{\log a} \ )$

$t \geq 4.512$

Thus, the number of years it will take for the laptop to be worth $600 or less is approximately 5 years.