The population of a colony of mosquitoes grows exponentially

The population of a colony of mosquitoes grows exponentially. There were 1000 mosquitoes in the colony initially and there were 1800 mosquitoes in the colony after 1 day. Write the model that gives the amount of mosquitoes in the colony at any time t. Exact values only (no decimals) in your model. for credit! Determine how long it will be until there are 10.000 mosquitoes in the colons Round your final solution to at least one decimal place. for credit! How much money will be in an account after 3 years if $400 is invested at an interest rate of 7% compounded continuously? Round your final solution to two decimal for credit!

Solution

11) initial population of mosquitoes = 1000

standard exponential equation is given by

y = ab^x

where a = initial population

y = 1000 (b)^x

there are 1800 mosquitoes after 1 day

finding the growth factor

1800 = 1000(b)^1

b = 1800 / 1000

b = 1.8

growth factor of mosquitoes = 18/10

hence equation becomes

y = 1000(18/10)^t

b) time it takes to reach population to 10,000

10,000 = 1000 ( 1.8)^t

dividing both sides by 1000

10 = 1.8^t

ln 10 = t ln 1.8

t = ln 10 / ln 1.8

t = 4 days approximately