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iren [92.7K]
3 years ago
5

If you write all of the whole numbers from 1 to 1000, how many numbers have the digit 4?

Mathematics
1 answer:
Simora [160]3 years ago
4 0
A.)
There are 400 4’s counting to one thousand
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In this example we modeled the world population from 1900 to 2010 with the exponential function P(t) = (1436.53) · (1.01395)t wh
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a) Rate of increase = 26.66 millions per year

b) Rate of increase = 42.64 millions per year

c) Rate of increase = 79.53 millions per year

Step-by-step explanation:

We are given that population is modeled with the exponential function:

P(t) = (1436.53).(1.01395)^t

where t = 0 corresponds to the year 1900 and P(t) is measured in millions.

Rate of increase of world population =

\displaystyle\frac{d(a^x)}{dx} = a^xln(a)\\\\P'(t) = (1436.53)(1.01395)^tln(1.01395)\\\\P'(t) = (1436.53)ln(1.01395)(1.01395)^t

a) 1920

P'(1920-1900) = (1436.53)(ln(1.01395))(1.01395)^{(1920-1900)}\\P'(20) = (1436.53)(ln(1.01395))(1.01395)^{(20)}\\P'(20) \approx 26.66

Rate of increase = 26.66 millions per year

b) 1955

P'(1955-1900)=(1436.53)(ln(1.01395))(1.01395)^{(1955-1900)}\\P'(55) = (1436.53)(ln(1.01395))(1.01395)^{(55)}\\P'(55) \approx 42.64

Rate of increase = 42.64 millions per year

c) 2000

P'(2000-1900) = (1436.53)(ln(1.01395))(1.01395)^{(2000-1900)}\\P'(100) = (1436.53)(ln(1.01395))(1.01395)^{(100)}\\P'(100) \approx 79.53

Rate of increase = 79.53 millions per year

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3 years ago
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