Question

In 2005, a laptop computer was purchased for $1900. Each year since, the resale value has decreased by 23%. Let t be the number of years since 2005. Let y be the value of the laptop computer, in dollars. Write an exponential function showing the relationship between y and t.

Answer 1

Answer:

$y=\ 1900(\frac{77}{100})^t$

Step-by-step explanation:

GIVEN: In $2005$, a laptop computer was purchased for $\ 1900$. Each year since, the resale value has decreased by $23\%$. Let $t$ be the number of years since $2005$.

TO FIND: Let $y$ be the value of the laptop computer, in dollars. Write an exponential function showing the relationship between $y$ and $t$.

SOLUTION:

value of laptop in $2005$ $=\ 1900$

decrease in resale value each year $=23\%$

resale value of laptop after each year $=100-23=77\%$

resale value after one year $=\frac{77}{100}\times\ 1900$

Now,

$y=\ 1900(\frac{77}{100})^t$

Hence relation between value of the laptop computer and time is

$y=\ 1900(\frac{77}{100})^t$

Answer 2

The exponential function showing the relationship between y and t should be $y = 1900(77\div 100)^t$.

Calculation of the exponential function:

Since

In 2005, a laptop computer was purchased for $1900. Each year since, the resale value has decreased by 23%.

Let t be the number of years since 2005.

Let y be the value of the laptop computer, in dollars.

So based on this, we can say that The exponential function showing the relationship between y and t should be $y = 1900(77\div 100)^t$.

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