Answer:
We choose B. (1, 10)
Step-by-step explanation:
Given the exponential model in the form y = a[tex]b^{x}[/tex]
<=> 50 = a[tex]b^{2}[/tex]
<=> a = [tex]\frac{50}{b^{2} }[/tex] (1)
<=> 250 = a[tex]b^{3}[/tex] (2)
Substitute (1) into (2) we have:
250 = [tex]\frac{50}{b^{2} }[/tex][tex]b^{3}[/tex]
<=> 50b = 250
<=> b = 5
=> a = [tex]\frac{50}{5^{2} }[/tex] = 2
Hence, our exponential model is: y =2* [tex]5^{x}[/tex]
Let analyse all possible answer:
A. (0, 5) we have: y =2* [tex]5^{0} =2[/tex] ≠ 5 so it is wrong
B. (1, 10) we have: y = 2* [tex]5^{1} =10[/tex] so it is true
C. (4, 450) we have: y = 2*[tex]5^{4} =1250[/tex] ≠ 450 so it is wrong
D. (5, 650) we have: y = 2*[tex]5^{5} =6250[/tex] ≠ 650 so it is wrong
Hence we choose B. (1, 10)
