Yellow-bellied Sunbirds Researchers31 have modeled the mass of a Yellow-bellied Sunbird t days after hatching using M= 8.6 divide 1 plus 8.55e exponent -037t. 

Here M is measured in grams. The hatchlings require parental care until they reach a mass of 7.5 grams.

a. Plot the graph of M along with the target value of 7.5 over the first 15 days.

The graph above shows the mass of a Yellow-bellied Sunbird over the first 15 days after hatching, modeled by the given function. The target mass of 7.5 grams, which the hatchlings must reach to no longer require parental care, is represented by the red dashed line. As the days progress, the mass of the bird approaches this target.

Would you like any further details or explanations?

Here are five related questions:
1. How long does it take for the sunbird to reach 7.5 grams based on the model?
2. What is the significance of the exponential decay term in the mass model?
3. How would the graph change if the constant 8.55 were different?
4. Can we calculate the mass of the bird after 20 days using the model?
5. How is this growth curve related to biological growth patterns in general?

**Tip:** Exponential models are often used in biology because they reflect rapid early growth that slows as organisms approach maturity.

Yellow-bellied Sunbirds Researchers have modeled the mass of a Yellow-bellied Sunbird t days after hatching using M = 8.6 / (1 + 8.55 * e^(-0.37t)). The hatchlings require parental care until they reach a mass of 7.5 grams. Plot the graph of M along with the target value of 7.5 over the first 15 days.

Explore how to model the growth of a Yellow-bellied Sunbird over the first 15 days using an exponential decay formula. This problem includes plotting the bird's mass and comparing it to the target of 7.5 grams. Suitable for students in Grades 9-12 studying algebra and exponential functions.

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