Magic Beans

7. Demonstrate how Jack used the model b(t) to calculate how high the beanstalk would be after 6 hours had passed. (You may use the table but write down where you would put the numbers in the function if you didn’t have the table.)

 $b\left(t\right)=3^t$  

•  $b\left(t\right)=3^t$  

•  $b\left(6\right)=3^6$  

•  $b\left(3\right)=3^3$  

8. During that same night, a neighbor was playing with his drone. It was programmed to hover at 243 ft. How many hours had the beanstalk been growing when it was as high as the drone?

• 59,049 feet

• 2 hours

• 5 hours

• 243 hours

10. While Jack was making his table, he was wondering how tall the beanstalk would be after the magical 10 hours had passed. He quickly typed the function into his calculator to find out. Write the equation Jack would have typed into his calculator.  

• b(10) = 3^10

• b(t) = 3^t

• b(3) = 10^3

• b(t) = 3^20

11. Commercial jets fly between 30,000 ft. and 36,000 ft. About how many hours of growing could pass before the beanstalk might interfere with commercial aircraft? 

12. Use the table to find  $\ f^{-1}\left(11,364\right)$  

12. Use the table to find  $f\left(7\right)$  

• 1,262

• 9

• 2,187

• 59,049

13. Use the table to find  $f\left(9\right)$  

13. Use the table to find  $f^{-1}\left(9\right)$