Question

felipe and trevon used the equation $y = 2 \cdot 1.5^x$, but it didnt break all the targets. felipe: we need to change the 2 to break them all. trevon: no, we need to change the 1.5. who do you think is correct? felipe trevon both neither explain your thinking. because the equation $y = 2 \cdot 1.5^x$ broke the first target (0,2), so we dont need to change the 2 and the graph shows the curve getting steeper. it means the base should be increased; therefore, we need to change the 1.5.

Explanation:

The equation is an exponential function \( y = a\cdot b^{x} \), where \( a \) is the initial value (when \( x = 0 \), \( y=a \)) and \( b \) is the growth factor. For the point \( (0,2) \), when \( x = 0 \), \( y=2\cdot1.5^{0}=2\cdot1 = 2 \), so the initial value (the 2 in the equation) is correct as it hits the point \( (0,2) \). To break more targets, we need to increase the growth rate, which is controlled by the base \( b \) (the 1.5 in the equation). So increasing the base (changing 1.5 to a larger number) will make the function grow faster and break more targets. Thus, Trevon is correct because the initial value (2) is already correct (hits \( (0,2) \)), and we need to adjust the growth factor (1.5) to make the function grow faster to break all targets.

Answer:

Trevon