The exponential function f(x)=4^x describes the number of bacteria in a population after x 30-minute intervals. In which interval will there first be more than 10,000 bacterium?

Question

a
8
b
5
c
6
d
7

Answer 1

b) 5

To find the interval in which there will first be more than 10,000 bacteria, we need to solve the exponential function for x:

4^x > 10,000

Taking the natural logarithm of both sides:

ln(4^x) > ln(10,000)

x * ln(4) > ln(10,000)

x > ln(10,000) / ln(4)

x > 5.68

Therefore, the interval in which there will first be more than 10,000 bacteria is after 5 intervals.