You Buy a Commemorative coin for $110. Each Year (t) the value (v) of the coin increases by 4%. Write an exponential model for this situation. Calculate the value of the coin after 3 years. When will the value of the coin will be $150?

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Answer 1 · 2016-11-03T22:45:11

Value after 3 years is $$ 123.74$ $$123.74$

After 7 years and 11 months the value will be $150

Use the formula for exponential growth, which is the same as for compound interest:

$V = P {(1 + \frac{R}{100})}^{t}$ $V = P(1 + R/100)^t$

$V = 110 {(1.04)}^{3} \leftarrow 4 %$ $V = 110(1.04)^3" "larr 4%$ increase per year for 3 years

$V = $ 123.74 \leftarrow$ $V = $123.74" "larr$ the value after 3 years.

When will the value be $150 ? \leftarrow$ $150?" "larr$ find t

$150 = 110 {(1.04)}^{t} \leftarrow \div 110$ $150 = 110(1.04)^t" "larr div 110$

$\frac{150}{110} = {1.04}^{t} \leftarrow$ $150/110 = 1.04^t" "larr$ log both sides

$log (\frac{15}{11}) = t \times log 1.04$ $log(15/11) = txxlog1.04$

$log (\frac{15}{11}) \div log 1.04 = t \leftarrow$ $log(15/11) div log 1.04 = t" "larr$ use a calculator

$7.9079 = t \approx 7 \frac{10.9}{12}$ $7.9079 = t ~~7 10.9/12$

After 7 years and 11 months the value will be $150