Question

Dean published his first novel at the beginning of July. By the end of July, he had sold 640 copies. In
August, he sold 800 copies. The book got great reviews in its first couple of months, so Dean expects his
sales to continue to increase.
Write an exponential equation in the form y = a(b)* that can model the monthly number of books sold,
y, x months after publishing.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
To the nearest whole number, how many books can Dean expect to sell during the month of December, 5
months after publishing?
books

Answer 1

Answer :

• 1,953

Explanation :

The exponential function is given by,

• y = a(b)^x

here,

• a = initial value
• b = growth rate
• y = no. of books sold
• x = time period

atq,

• a = 640
• b = (books sold during 2nd month)/(books sold during 1st month) = 800/640 = 1.25
• y = ?
• x = 5

plugging in the values,

• y = 640(1.25)^5
• y = 640*3.05175..
• y ≈ 1,953

therefore, Dean would have sold nearly an amount of 1,953 books by December.

Answer 2

Answer:

1953 books

Step-by-step explanation:

To model the monthly number of books sold, $y$, $x$ months after publishing, we can use an exponential equation in the form:

$\Large \boxed{\boxed{y = a \cdot b^x}}$,

where:

• $a$ represents the initial number of books sold.
• $b$ represents the growth rate or multiplicative factor.

Given the information:

• In July (the first month), Dean sold 640 books.
• In August (the second month), Dean sold 800 books.

We can use these data points to find the values of $a$ and $b$.

• Use July's data: $a = 640$.
• Use August's data: $800 = a \cdot b^1$ (since August is the second month).

Now, we can solve for $b$:

$b = \dfrac{800}{a} \\\\= \dfrac{800}{640} \\\\= \dfrac{5}{4} = 1.25$

Therefore, our exponential equation becomes:

$y = 640 \times (1.25)^x$

To find the number of books Dean can expect to sell in December (5 months after publishing), substitute $x = 5$ into the equation:

$y = 640 \times (1.25)^5$

$y \approx 640 \times 3.051757813$

$y \approx 1953.125$

$y \approx 1953\textsf{ (in nearest whole number)}$

To the nearest whole number, Dean can expect to sell approximately 1953 books during the month of December, 5 months after publishing.