Let's solve the given exponential function [tex]\( A(t) = 150 \times (1.05)^7 \)[/tex] step by step.
1. Identify the parameters of the function:
- The initial amount is [tex]\( 150 \)[/tex].
- The growth rate is [tex]\( 1.05 \)[/tex].
- The time period is [tex]\( 7 \)[/tex].
2. Exponentiation:
- We need to raise the growth rate [tex]\(1.05\)[/tex] to the power of [tex]\(7\)[/tex]. This exponentiation is part of evaluating the exponential function.
3. Multiplication:
- Multiply the initial amount [tex]\(150\)[/tex] by the result of the exponentiation to get the final amount.
4. Round to the nearest hundredth:
- Once we get the final amount from the multiplication, we round it to the nearest hundredth place for precision.
After following these steps, the calculation gives us a final amount of approximately [tex]\(211.06506339843756\)[/tex]. When we round this to the nearest hundredth, it becomes [tex]\(211.07\)[/tex].
Therefore, the best answer is:
B. 211.07
