The value of an investment follows a pattern of exponential growth. In the year

Question

The value of an investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment 1 years after 2000 is given by exponential growth model A = 7800e^0.0471. How much did you initially invest in the account? $3900.00 $8175.35 $366.60 $7800.00 The value of an investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model A = 3900e^0.069t. By what percent did the account each year? 7.5% 6.9% 7.6% 7.3% The population of a particular country was 28 million in 1980; in 1992 it was 32 million. The exponential growth function A = 28e^kt describes the population of this country t years after 1980. Use the fact that 12 years after 1980 the population increased by 4 million to find k to three decimal places. 0.011 0.021 0.116 0.566

Explanation / Answer

1) pattern is given by

A = 7800 e^.047t

to find initial value plug t=0

A = 7800 e^0 = 7800

so, initial investment was $ 7800

2) A = 3900 e^.069t

standard exponential equation is given by

A = Ao e^rt

where , r is the growth rate

comparing the two equations we get

r = .069

multiply the value by 100 to get the percentage growth each year

.069*100 = 6.9%

3) A = 28e^kt

in 1992 population was 32 million

so in 12 years population became 32

plugging the value in the formula

32 = 28 e^12k

32/28 = e^12k

1.142 = e^12k

ln 1.142 = 12k ln e

k = .0111

( option 1)

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