Final answer:
Natalie's mother will donate $90 to charity if Natalie bikes 30 miles.
Step-by-step explanation:
If Natalie bikes 30 miles, and her mother pledges $1.50 for every 0.5 miles, we can calculate the donation amount by first determining how many 0.5-mile segments there are in 30 miles. We do this by dividing 30 miles by 0.5:
30 miles ÷ 0.5 mile/segment = 60 segments
Now, we multiply the number of segments by the pledge amount per segment:
60 segments × $1.50/segment = $90
Therefore, Natalie's mother will donate $90 to charity.