N = 5000(1.5)^h/40 Word Problem (Math 10 / Pre Calc)

Question

The N is supposed to indicate the number of bacteria (N = 5000)

1.5 just means every 40 h it will increase by 1.5

So my question ask, "How much bacteria are there after 40 h?" then asks "how many more bacteria are the after 3h"

so for the first part of the question its 5000 x 1.5 = 7500, but for the second part is very confusing. I looked at the answer key and it was for some reason "154 more bacteria after 3h"

Answer 1

5000(1.5)^(3/40) = 5000(1.5)^.075 =about 5154

an increase of 5154-5000= 154

1.5^.075 requires a calculator

it equals 1.030876986

multiply that by 5000 to get 5154.384932

subtract 5000 to get 154.384932

round off