Question

which of the following data points would not satisfy the exponential model $f(x)=3(2)^x$
a. $\bigcirc$ $(2,12)$
b. $\bigcirc$ $(0,3)$
c. $\bigcirc$ $(4,30)$
d. $\bigcirc$ $(3,24)$

Explanation:

Step1: Check point A (2,12)

Substitute \( x = 2 \) into \( f(x)=3(2)^x \): \( f(2)=3(2)^2 = 3\times4 = 12 \). So (2,12) satisfies the model.

Step2: Check point B (0,3)

Substitute \( x = 0 \) into \( f(x)=3(2)^x \): \( f(0)=3(2)^0 = 3\times1 = 3 \). So (0,3) satisfies the model.

Step3: Check point C (4,30)

Substitute \( x = 4 \) into \( f(x)=3(2)^x \): \( f(4)=3(2)^4 = 3\times16 = 48
eq 30 \). So (4,30) does not satisfy the model.

Step4: Check point D (3,24)

Substitute \( x = 3 \) into \( f(x)=3(2)^x \): \( f(3)=3(2)^3 = 3\times8 = 24 \). So (3,24) satisfies the model.

Since the question asks which data point would NOT satisfy the model, we identify that point C (4,30) does not fit.

Answer:

C. (4,30)