It seems you've uploaded an image. Let me extract the relevant information and provide assistance. I'll process it now. PIL import Image

Load the image to inspect its contents

img_path = '/mnt/data/1733729015323d2qw79u4.jpg' image = Image.open(img_path)

Display image to check

image.show()It seems that I've displayed the image, but I will now proceed to extract any relevant mathematical details from it. Let me analyze the image content further. Attempt to use OCR (Optical Character Recognition) to extract text from the image import pytesseract

Extract text from the image

extracted_text = pytesseract.image_to_string(image)

extracted_textThe text extracted from the image refers to a problem involving exponential decay and the graph of a function. Here's a summary of the key elements:

1. Initial Value: The question asks for the initial value of $Q$ when $t = 0$.
2. Decay Rate: The graph indicates a continuous decay rate, and the question asks for this rate.
3. Time when $Q = 4$: You are asked to estimate the time $t$ when $Q(t) = 4$ from the graph.
4. Exact Time Calculation: The final part involves using logarithms to determine the exact value of $t$ when $Q = 4$.

To proceed, I can help with:

• Estimating the initial value and decay rate from the graph.
• Using logarithms to solve for the exact time $t$ when $Q(t) = 4$.

Would you like me to focus on one part of the problem or walk through all of them? Feel free to specify any part you'd like more help with!