# 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?

Nov 3, 2016

Value after 3 years is $123.74 After 7 years and 11 months the value will be$150

#### Explanation:

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

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

V = 110(1.04)^3" "larr 4% increase per year for 3 years

V = $123.74" "larr the value after 3 years. When will the value be 150?" "larr find t $150 = 110 {\left(1.04\right)}^{t} \text{ } \leftarrow \div 110$$\frac{150}{110} = {1.04}^{t} \text{ } \leftarrow$log both sides $\log \left(\frac{15}{11}\right) = t \times \log 1.04$$\log \left(\frac{15}{11}\right) \div \log 1.04 = t \text{ } \leftarrow$use a calculator $7.9079 = t \approx 7 \frac{10.9}{12}$After 7 years and 11 months the value will be$150