Question

On Monday, your English teacher gives you a list of twenty-five vocabulary terms to be memorized. You memorize all of them Monday night and do not look at the list again. Because you do not study again, you forget 6% of the list each day.a. Does this problem represent exponential growth or decay? How do you know?b. Which exponential formula below will you use for this problem? Why?(Your choices are f(x) = a (1 + r) or f(x) = a (1-ry')c. Write the formula for this specific problem. Explain how you know where each number goes in the formula.d. How many terms will you remember seven days later for the test? Show all your work and explain your computations.

Answer 1

a. Exponential decay

b. f(x) = a (1 - r)^x

c. f(x) = 25(1 - 0.06)^x

d. 16 terms

Step-by-step explanation:

a. Does this problem represent exponential growth or decay? How do you know?

Each day the number of terms that you know is less than the day before, so there is a decrease in the vocabulary terms memorized. It means that the problem represents exponential decay.

b. Which exponential formula below will you use for this problem? Why?

The formula for the exponential decay is:

`f(x)=a(1-r)^x`

Where a is the initial value and r is the rate of decay.

So, the formula that you will use is f(x) = a (1 - r)^x

c. Write the formula for this specific problem. Explain how you know where each number goes in the formula.

The initial value is 25 terms and the decay rate is 6%, so the specific equation is:

`f(x)=25(1-0.06)^x`

d. How many terms will you remember seven days later for the test? Show all your work and explain your computations.​

Now, we need to replace the value of x by 7, so:

`\begin{gathered} f(7)=25(1-0.06)^7 \\ f(7)=25(0.94)^7 \\ f(7)=25(0.6485) \\ f(7)=16.21 \end{gathered}`

Therefore, you will remember 16 terms seven days later.