Question
Question The number of ripened grape tomatoes grows exponentially starting in the eighth week. In week 8 there were 16 ripe tomatoes and in week 9 there were 30 ripe tomatoes. What is the growth factor? Provide your answer below: \( \square \)
Ask by Conner Morrison. in the United States
Feb 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The growth factor is 1.875.
Solution
The growth factor is found by dividing the number of tomatoes in week 9 by the number in week 8. That is:
Growth factor = 30 / 16 = 15/8 = 1.875
So, the growth factor is 1.875.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To find the growth factor, we can use the formula for exponential growth: \( N(t) = N_0 \times r^t \), where \( N(t) \) is the amount at time \( t \), \( N_0 \) is the initial amount, \( r \) the growth factor, and \( t \) the number of time intervals. Here, at week 8 (\( N_0 \) = 16) and at week 9 (\( N(1) \) = 30). We can set up the equation: \( 30 = 16 \times r^1 \) Now, solving for \( r \): \( r = \frac{30}{16} = 1.875 \) So, the growth factor is \( 1.875 \). \( \square \) 1.875
