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ID: 3019040 • Letter: S
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soep 152222 o the tavoriters bar by selecting &o; by getting them from another browser. Import your tavoites te modeled by P-150 4c". where r represents the year, with 0 corresponding to 2000 In 2007, the population The population P n thousands) of a cestain city from of the city was about 167,075 (a) Find the vohe of (Round your answer to four decimal places because k is positive, the population is decreasing O Because k is negative, the population is Increasing. 0 Because k ks negative, the population-s decreasing Because k is positive, the population is increasing (th) Use the model to predict the populations of the city On thousands) in 2020 and 2025. (Round your ansmers to three decimal places. 2020 p-m2M641w]× thousand people 2025P-265125353 73 x thousand people Are the resits rea-snableExplor The popdal es are not reasonitle. The population carrot (entine to name the-rate uti ten the vee jaaie aan. The populations are reenonable if R continues to ncrease at the same rate from the year 2020 to 2023 Acconding to the model, during whst year will the populstion reach 230ono US20LTOO9
Explanation / Answer
given P=150.4ekt,P in thousands
(a)t=0 for year 2000
so for year 2007 ,t=7
=>150.4ek*7=(167075/1000)
=>k=(1/7)ln(167075/150400)
=>k=0.01502062884
=>k=0.0150
because k is positive ,the population is increasing
-----------------------------
(b)
in 2020, t=20
=>P=150.4e0.01502062884*20
=>P= 203.102 thousand people
in 2020, t=20
=>P=150.4e0.01502062884*25
=>P= 218.944 thousand people
the populations are reasonable if it continues to increase at the same rate from the year 2020 to 2025
(c)
population is 230000
=>P=230
=>150.4e0.01502062884*t=230
=>t=28.2798
in 29th year after 2000
year =2029
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