Answer:
2) V = 2000·1.07^t; $6317.63 after 17 years
3) D = 950·0.82^t; 2 months to a balance of $650
Step-by-step explanation:
Exponential equations are not so difficult. They are generally of the form ...
f(t) = (initial value) × (growth factor)^t
where t is the number of time periods to which growth factor applies. (I problem 2, that is years; in problem 3, that is months.)
The growth factor can be written different ways. In terms of growth rate, it is ...
growth factor = 1 + growth rate
Often, the growth rate is expressed as a percentage. It may be positive or negative.
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2) The initial value is $2000, and the growth rate is 7% = 0.07. So, the exponential equation for value is ...
V = 2000·1.07^t
The value after 17 years is ...
V = 2000·1.07^17 = 6317.63
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3) The initial value is $950, and the growth rate is -18% = -0.18. That means the growth factor is 1-0.18 = 0.82. So, the exponential equation for the remaining debt is ...
D = 950·0.82^t . . . . . where t is in months
We want to find the value of t when D=650, so we put that in the equation and solve for t. Logarithms are required.
650 = 950·0.82^t
650/950 = 0.82^t . . . . . . . . . . divide by 950
log(650/950) = t·log(0.82) . . . take logarithms
log(650/950)/log(0.82) = t ≈ 1.91
It will take about 2 months for the balance to be about $650.
