How do I find k and the number of hits after 24 months?

Question

The number of y hits a new website receives each month can be modeled by y=4030e^kt, where t represents the number of months the website has been operating. In the websites third month, there were 9000 hits. Find value of k and round it to four decimal places. Use this value to predict number of hits website will receive after 24 months and round to nearest whole number.

Answer 1

The number of y hits a new website receives each month can be modeled by y=4030e^kt, where t represents the number of months the website has been operating. In the websites third month, there were 9000 hits. Find value of k and round it to four decimal places. Use this value to predict number of hits website will receive after 24 months and round to nearest whole number.

When t = 3, y = 9000, so,

9000 = 403e^3k divide by 403

22.3325 = e^3k put the exponential equation into log form,

ln 22.3325 = 3k

3.1060 = 3k divide by 3

k = 1.0353 Substitue this for k, and use 24 for t in the original equation.